TASKS FOR FINDING THE UNKNOWN BY TWO DIFFERENCES

Consider an example of solving the problem of finding the unknown by two differences.

A task: The two cars were moving at the same speed. One traveled 400 km and the other 480 km. The second car was on the road 2 hours less than the first. How many hours was each car on the road?

Solution:

1. Find the difference in the distances traveled by cars:

480 - 400 = 80 km

2. The second difference is known to us from the condition of the problem - it is 2 hours (the difference in travel time).

3. Based on these two differences, we calculate the speed of the cars:

80 ÷ 2 = 40 km/h.

4. Knowing the speed of the cars and the distances traveled by each car, we find the travel time for each car:

400 ÷ 40 = 10 hours - travel time of the first car;

480 ÷ 40 = 12 hours - travel time of the second car.

Answer: 10 and 12.

Examples of tasks for finding the unknown by two differences for training:

1) In the dining room in the 1st hall there are 15 identical tables, and in the 2nd hall there are 10 of the same tables. How many seats are in the 1st hall and how many are in the 2nd hall, if there are 20 more seats in the 1st hall than in the 2nd hall?

2) One driver made 5 trips per day, the other - 3 trips. In each flight, grain was transported equally. The first driver transported 30 tons more grain than the second. How much grain did each driver carry?

3) Bought 5 red pencils and 7 blue ones. Blue ones are 4 rubles more expensive than red ones. How much does one red and one blue pencil cost?

4) In one piece there were 6 m of fabric, and in the other - 12 m of the same fabric. The second piece cost 24 rubles. more expensive than the first. How much did each piece of fabric cost?

5) In the first piece 3 m of fabric, in the second - 7 m of fabric. The second piece costs 240 rubles more. How much is each piece?

6) One motorcyclist was on the road for 3 hours, the other for 5 hours. They were traveling at the same speed. The second traveled 80 km more than the first. How many kilometers did each travel?

7) From the base, 3 truckloads of flour were sent to one store, and 5 truckloads to another. 40 q more were sent to the second store. How many centners of flour were sent to each store?

8) 25 sacks of onions were collected from one plot, and 19 sacks from another. 360 kg less was collected from the second plot. How many kilograms of onions were collected from each plot?

9) The store sold 72 kg of plums on the 1st day, and 56 kg on the 2nd. On the 2nd day sold 2 boxes less than on the 1st day. How many crates of plums were sold each day?

10) Two cyclists rode towards each other with the same speed and met after 10 hours. One drove 2 hours more than the other before the meeting and drove 24 km more. What is the distance between cities?

11) There were two pieces of cloth in the workshop, 96 m and 84 m long. Raincoats were sewn from them. From the 2nd piece, we received 3 cloaks less than from the 1st piece. How many cloaks are made from each piece?

12) There are 48 hives in one apiary, and 44 in the other. 80 kg were removed from the 1st apiary more honey than from the 2nd. How much honey was collected from each apiary?

Tasks for finding the unknown by two differences with answers Grade 4

2099) 320 kg of potatoes and 960 kg of carrots were harvested. Potatoes turned out 80 bags less than carrots. How many bags of potatoes and how many carrots?
2100) In total, the boy poured 12 liters more into the barrel than the girl. How many liters of water did each bring?
2101) Two trains left two cities towards each other with the same speed and met 6 hours after the second train left. The first train left 3 hours earlier and traveled 186 km more. What is the distance between cities?
2102) On one road from the village to the village can be reached in 3 hours. On the other - at the same speed - in 5 hours, since the second road is 92 km longer. What is the length of each road?
2103) 24 sacks of potatoes were brought to one store, and 28 sacks were brought to another. The second store brought 160 kg more than the first. How many kilograms of potatoes were brought to each store?
2104) Dad bought 3 kg of bananas and 5 kg of apples for the same price. He paid 12 rubles for apples. more. How much does the whole purchase cost?
2105) How many kilograms of grain were spent in each month? (March has 31 days, February has 28 days.)
2106) There are 120 m of fabric in one piece. In the other - 85 m of the same fabric. The first piece for 1050 rubles. expensive. How much does the whole fabric cost?
2107) one worker worked 5 days and the other worked 7 days The first worker earned 80 rubles. less. How much did each earn?
2108)*Collected several crates of apples and the same number of crates of pears. Each crate of apples weighs 3 kg more than a crate of pears. In total, 24 kg more apples were harvested than pears. How many crates of pears and apples did you collect?
2109)* The same number of boxes of bananas and oranges were brought to the store. Only 96 kg. One box of bananas is 2 kg heavier than a box of oranges, and their total weight is 24 kg more than the oranges. How many kilograms of bananas and how many oranges did you bring?
2110) Dresses were sewn from 56 m of blue and 44 m of green fabric. There were 3 more blue dresses than green ones. How many blue and how many green dresses were made?
2111) There are 15 identical tables in the dining room in the first room, and 10 identical tables in the second room. How many seats are there in the first hall and how many in the second hall, if there are 20 more seats in the first hall than in the second?
2112) The first piece has 3 meters of fabric, the second - 7 meters. The second piece costs 240 rubles. expensive. How much is each piece?
2113) There are 15 identical tables in the dining room in the first room, and 10 of the same tables in the second room. How many seats are at each table if there are 20 more seats in the first room than in the second room?
2114) In each flight, grain was transported equally. The first driver transported 30 tons more than the second. How much grain did each driver carry?
2115) For the blue ones they paid 6 rubles. more than red ones. How much is 1 red and 1 blue pencil?
2116) The first piece contained 6 meters of cloth, and the second piece contained 12 meters of the same cloth. The second piece cost 24 rubles. more expensive than the first. How much did each piece of fabric cost?
2117) The first motorcyclist was on the road for 3 hours, the second for 5 hours. The second traveled 80 km more than the first. How many kilometers did each travel?
2118) 3 trucks of flour were sent from the base to the first store, and 5 truckloads of flour to the other. 40 q more were sent to the second store. How many centners of flour were sent to each store?
2119) two cars were walking at the same speed One traveled 400 km and the other 480 km. The second car was on the road 2 hours less than the first. How many hours was each car on the road?
2120) 25 sacks of onions were harvested from one plot, and 19 sacks from another. 360 kg less was collected from the second plot. How many kilograms of onions were collected from each plot?
2121) The store sold 72 kg of plums on the first day, and 56 kg on the second. On the second day, 2 boxes were sold less than on the first day. How many crates of plums were sold each day?
2122) In the workshop there were 2 pieces of cloth, 96 m and 84 m long. Raincoats were sewn from them. From the second piece we received 3 less cloaks than from the first piece. How many cloaks are made from each piece?
2123) Two cyclists rode towards each other at the same speed and met 4 hours after the departure of the second, who left 2 hours later and traveled 14 km less than the first before meeting. What is the distance between cities?
2124) There are 48 hives in one apiary, and 44 in another. From the first apiary, 80 kg more honey was collected than from the second How much honey was collected from each apiary?
2125) One worked 5 minutes and the other 8 minutes. How much water did each pump pump out if the second pumped out 15 buckets more than the first pump?
2126) One bag contains 54 kg of flour, and the other contains 72 kg. Flour was scattered into bags. From the first bag it turned out 6 bags less. How many bags of flour were made from two bags?
2127) On the second day, she was on the road 2 hours less than on the first. How many hours was the car on the road?
2128) more than a boy. How much money did each spend?

Task 1

Two cars were traveling at the same speed. One of them traveled 400 km and the other 480 km. How many hours was each car on the road if the first was on the road 2 hours less than the second?

Solution:
• 1) 480 - 400 = 80
• 2) 80: 2 = 40 (vehicle speed)
• 3) 400: 40 = 10 (the first car was on the way)
• 4) 480: 40 = 12 (second car was on the way)
• Answer: 10 and 12 hours.

Task 2

Two motorcyclists were traveling at the same speed. One of them was on the road for 5 hours and the other for 3 hours. How many kilometers did each motorcyclist drive if the first rider traveled 80 kilometers more than the second?

Solution:
• 1) 5 - 3 = 2
• 2) 80: 2 = 40 (speed of each rider)
• 3) 5 * 40 = 200 (the first motorcyclist passed)
• 4) 3 * 40 = 120 (the second motorcyclist passed)
• Answer: 200 and 120 kilometers.

Task 3

The dressmaker bought two pieces of fabric. One piece is 6 meters and the other is 12 meters. She paid 24 rubles less for the first piece than for the second. How much did the dressmaker pay for each of the pieces of fabric, if a meter of fabric costs the same in each of the pieces?

Solution:
• 1) 12 - 6 = 6
• 2) 24: 6 = 4 (it costs a meter of fabric)
• 3) 6 * 4 = 24 (the first piece is worth)
• 4) 12 * 4 = 48 (the second piece is worth)
• Answer: 24 and 48 rubles.

Task 4

Two drivers were carrying grain. One of them made 3 flights, the other - 5 flights per day. The second driver transported 30 tons more grain than the first. How much grain was transported by each of the drivers separately, if each flight carried the same amount of grain?

Solution:
• 1) 5 - 3 = 2
• 2) 30: 2 = 15 (tonnes of grain were transported by one truck per trip)
• 3) 3 * 15 = 45 (the first truck transported tons of grain)
• 4) 5 * 15 = 75 (the second truck transported tons of grain)
• Answer: 45 and 75 tons.



Task 5

In the dining room in one of the halls there are 15 identical tables, in the other hall there are 10 of the same tables. How many seats are there in the first hall and in the second hall separately, if there are 20 fewer seats in the second hall than in the first?

Solution:
• 1) 15 - 10 = 5
• 2) 20: 5 = 4 (seats at one table)
• 3) 15 * 4 = 60 (seats in the first hall)
• 4) 10 * 4 = 40 (seats in the second hall)
• Answer: 60 and 40 seats.

Task 6

Sasha was bought 7 green pencils and 5 orange ones. Orange pencils are 4 rubles cheaper than green ones. How much does one green and one orange pencil cost?

Solution:
• 1) 7 - 5 = 2
• 2) 4: 2 = 2
• Answer: 2 rubles.

Task 7

The first piece has 3 meters of fabric, and the second has 7 meters. The first piece costs 240 rubles less than the second. How much does each piece cost separately, if a meter of fabric in each piece costs the same?

Solution:
• 1) 7 - 3 = 4
• 2) 240: 4 = 60 (it costs a meter of fabric)
• 3) 3 * 60 = 180 (the first piece costs rubles)
• 4) 7 * 60 = 420 (the second piece costs a ruble)
• Answer:

Task 8

Trucks transported flour from the base to two different stores. 3 trucks of flour were delivered to the first store, and 5 to the second. How many centners of flour were sent to each store separately, if flour was sent to the first store 40 centners less than to the second?

Solution:
• 1) 5 - 3 = 2
• 2) 40: 2 = 20 (quintals of flour were carried by a truck at a time)
• 3) 3 * 20 = 60 (taken to the first store)
• 4) 5 * 20 = 100 (taken to the second store)
• Answer: 60 and 100 centners.

Task 9

Onions were harvested in two plots. 19 bags were collected from one, and 25 from the other. How many kilograms of onions were collected from each site, if 360 kg less was collected from the first than from the second?

Solution:
• 1) 25 - 19 = 6
• 2) 360: 6 = 60 (kilogram of onion in 1 bag)
• 3) 19 * 60 = 1140 (kg of onions were collected from the 1st site)
• 4) 25 * 60 = 1500 (kg. Sobal onion from the 2nd section)
• Answer: 1140 and 1500 kilograms.