Critical Sum of Speed Time and Distance Class 7

Question 1. The distance between station A and B is 120 km. A train travelling at a speed can cover the distance in 2 hours 30 minutes. By how many km/h should the speed of the train be increased for it to take 30 minutes less to cover the distance. ?

Solution 1.
Case 1:
Data given:
Distance between station A and B = 120 km
Time taken by the train = 2 h 30 minutes
=(2+30/60) h
=5/2 h
Speed S1 of the train in km/h = D/S
=120/(5/2)
=48 km/h
Case 2:
Distance between station A and B = 120 km
Time taken by the train = 2 h
Speed S2 of the train = 120/2
=60 km/h Increased speed (S2-S1) = (60-48) km/h
=12 km/h Ans.

Question 2. Two trains start from the same staion in the smae direction. The speed of the first train is 70 km/h and that of the second train is 20 m/s. 1) Which train is moving faster ?
2) What is the distance between the trains after 1 hour and 15 minutes ?

Answer 2. Speed of the first train = 70 km/h
Speed of the second train = 20 m/s
i)Speed of the second train in km/h= 20x(18/5)
= 72 km/h
Therefore the second train is moving faster.
ii) Time = 1 h 15 m
=(1+15/60)h
=1+1/4 h
5/4 h
Distance covered by the first train= DXS
=70 X 5/4
87.5 km
Distance covered by the second train in the same time = D X S
= 72 X 5/4 km
90 km
Therefore the distance between two train after 1 h 15 minutes will be (90-87.5 ) km
=2.5 km Ans.

Question 3. Mohan could run a 100-m race in 20 seconds. After training , he can finish the race in 15 seconds. By how much has he improved his speed? ?

Answer 3. Speed of Mohan = D/ S
=100/20
5 m/s
Time taken to complete the race after training = 15 s
Speed of Mohan after training = 100/15 m/s
20/3 m/s
Improvement = (20/3 -5 )
=5/3 m/s
1 2/3 m/s or 1.67 m/s Ans.