Rajan travels 150 km by car, 620 km by train and 90 km by bus. The total time taken for the journey is one day and five hours. How much time is taken by the train to cover 286 km if the ratio of the speeds of the car, bus and train is 1:2:5?
Answers
Explanation:
Rajan travels 150 km by car, 620 km by train and 90 km by bus. The total time taken for the journey is one day and five hours. How much time is taken by the train to cover 286 km if the ratio of the speeds of the car, bus and train is 1:2:5?
=860km
Given:
Rajan travels 150 km by car, 620 km by train, and 90 km by bus.
the ratio of the speeds of the car, bus and train is 1:2:5
To Find:
How much time is taken by the train to cover 286 km?
Solution:
Let the speed of the car be x km/hr,
then the speed of the bus will be 2x km/hr,
and the speed of the train will be 5x km/hr.
⇒ Total distance travelled= 150 + 620 + 90 =860 km
⇒ Total time taken = 1 day 5 hours = 24 + 5 = 29 hours
⇒ time taken by car will be 150/x hours
⇒ time taken by train will be 620/5x hours
⇒ time taken by bus will be 90/2x hours
⇒total time taken = ( 150/x + 620/5x + 90/2x )hours
= ( 1500 + 1240 + 450 ) / 10x
= 3190 / 10x
⇒ 3190/10x = 29
⇒ 3190 = 290x
⇒ 3190/290 = x
⇒ x = 11
so the car= 11 km/hr
bus = 22 km/hr
train = 55 km/hr
So, the time taken by train to travel 286 km =
⇒ 286/55
⇒ 5.2 hr
⇒ 5 hour 12 mimutes
Hence, train cover 286 km in 5 hours 12 minutes.