Page 148 - Maths Skills - 8

146 Maths

\ Difference in time taken = (15x – 12x) min = 3x min

But, the actual difference in time = (9 + 6) min = 15 min
Now, when the difference in time taken is 3x minutes, the distance to school is x km.
x
When the difference in time taken is 1 minute, the distance to school is km.
3x
x
When the difference in time taken is 15 minutes, the distance to school is 3x × 15 km = 5 km.
Hence, the distance to his school is 5 km.

Example 6: Two trains of lengths 150 m and 120 m are moving in opposite directions, on parallel lines, one at
a speed of 72 km/h and the other at a speed of 36 km/h. In what time will they cross each other?
5
Solution: Relative speed of the trains = (72 + 36) km/h = 108 km/h = 108 × m/s = 30 m/s
18
 Total distance to be covered = Sum of the lengths of the trains = 150 m + 120 m = 270 m
Total distance to be covered 270 m
\ Time taken to cross each other = = = 9 s
Relative speed 30 m/s
Hence, the trains will cross each other in 9 seconds.

Example 7: Two trains 150 m and 120 m long are moving in the same direction at 72 km/h and 36 km/h
respectively on parallel tracks. How long would it take the faster train to cross the slower train?
5
Solution: Relative speed = (72 – 36) km/h = 36 km/h = 36 × m/s = 10 m/s
18
Total distance to be covered = Sum of the lengths of the trains = 150 m + 120 m = 270 m
Total distance to be covered 270 m
\ Time taken to cross each other = = = 27 s
Relative speed 10 m/s

Hence, the faster train will cross the slower train in 27 seconds.

Example 8: A 450 m long train is moving at 54 km/h. In what time will it cross an electric pole?
Solution: Total distance covered by the train = The length of the train = 450 m
5
Speed = 54 km/h = 54 × m/s = 15 m/s
18
Distance 450 m
\ Time = = = 30 s
Speed 15 m/s
Hence, the train will cross the electric pole in 30 seconds.

Example 9: The speed of a train is 72 km/h. How much time will it take to cross a bridge of 200 m if the length
of the train is 600 m?
Solution: Total distance to be covered = Length of the train + Length of the bridge = (600 + 200) m = 800 m
5
Speed = 72 km/h = 72 × m/s = 20 m/s
18
Distance 800 m
\ Time = = = 40 s
Speed 20 m/s

Hence, the train will cross the bridge in 40 seconds.