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Question
To reach Allahabad from Delhi , Ved travels 600 km , partly by train and partly by car. He would take 8 hours, if he travels 120 km by train and remaining distance by car. On the other hand , if he travels 200 km by train and remaining by car, then he would take 20 minutes longer than the first case. Find the speeds of the train and car. Consider that the train and car travel with a uniform and the same speed each time .
To reach Allahabad from Delhi , Ved travels 600 km , partly by train and partly by car. He would take 8 hours, if he travels 120 km by train and remaining distance by car. On the other hand , if he travels 200 km by train and remaining by car, then he would take 20 minutes longer than the first case. Find the speeds of the train and car. Consider that the train and car travel with a uniform and the same speed each time .
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Solution
Le the speed of the train be x km/hr and speed of car be y km/hr
Vijay travels 120 km by train, the distance covered by car 600-120 = 480 km
Now, time taken to cover 120 km by train = 120/xhr
And time taken to cover 480 km by car = 480/y
Total time taken to travel 600 km = 120/x + 480/y = 8 hr (i)
Similarly
200/x + 400/y = 8hr. 20minute = 8(20/60) (ii)
solve (i) and (ii)
we get
x = 60 km/hr and y = 80 km/hr
So speed of train is 60km/h and
Speed of car is 80 km/h
Vijay travels 120 km by train, the distance covered by car 600-120 = 480 km
Now, time taken to cover 120 km by train = 120/xhr
And time taken to cover 480 km by car = 480/y
Total time taken to travel 600 km = 120/x + 480/y = 8 hr (i)
Similarly
200/x + 400/y = 8hr. 20minute = 8(20/60) (ii)
solve (i) and (ii)
we get
x = 60 km/hr and y = 80 km/hr
So speed of train is 60km/h and
Speed of car is 80 km/h
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