A man travels 400 km partly by train and partly by car. If he covers 240 km by train and rest by car, it takes 6 hours. But if he travels 180 km by train and rest by car, he takes 15 minutes lesser. Find the speed of the train and that of the car.
Answers
Answer:
Train = 60 km/hr
Car = 80 km/hr
Step-by-step explanation:
Given that,
A man travels 400 km.
He travels the distance by train and car.
To find the speed.
Let the speed of train be x km/hr and that of car is y km/hr.
We know that,
Speed = Distance/Time
=> Time = Distance/Speed
Now, in first case, we have,
Distance by train = 240 km
Distance by car = (400-240) = 160 km
Time taken = 6 hr
Therefore, we have,
=> 240/x + 160/y = 6 ......(1)
Now, in second case, we have,
Distance by train = 180 km
Distance by car = (400-180) = 220 km
Time taken = 6 - 15/60 = 6-¼ = 23/4 hr
Therefore, we will get,
=> 180/x + 220/y = 23/4 ......(2)
Multiplying eqn (1) with 3 and eqn (2) with 4 and subtracting, we get,
=> 480/y - 880/y = 18 - 23
=> (880-480)/y = 23 - 18
=> 400/y = 5
=> y = 400/5
=> y = 80
Substituting this value in eqn (1), we get,
=> 240/x + 160/80 = 6
=> 240/x = 6 - 2
=> x = 240/4
=> x = 60
Hence, the speed of the train and that of the car is 60 km/hr and 80 km/hr respectively.
Answer:
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