Rahul spends his summer vacations at his Nani’s house, which is 500 km away from his
home. The train only travels up to 300 km. So his Nani drives 200 km to pick him up from
the station. Thus, it takes him 10 hours to reach his Nani’s house. But if he travels 200 km
by train and the remaining distance by car, he will arrive in his Nani’s house 50 minutes
earlier. Find the speed of the train and the car
Answers
Answer:
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Given : Rahul spends his summer vacations at his Nani’s house, which is 500 km away from his home.
The train only travels up to 300 km. So his Nani drives 200 km to pick him up from the station.
Thus, it takes him 10 hours to reach his Nani’s house.
But if he travels 200 km by train and the remaining distance by car, he will arrive in his Nani’s house 50 minutes earlier.
To Find : the speed of the train and the car
Solution:
Distance = Speed * Time
Train Speed = x km/hr
Car speed = y km/hr
300/x + 200/y = 10 hrs Eq1
50 minutes earlier. => time taken = 10 - 50/60 = 10 - 5/6 = 55/6 hrs
200/x + 300/y = 55/6 hrs Eq2
3 * Eq1 - 2 * Eq2
=> 500/x = 30 - 55/3
=> 500/x = 35/3
=> x = 1500/35
=> x = 300/7 km/hr
3 * Eq2 - 2 * eq1
=> 500/y = 55/2 - 20
=> 500/y = 15/2
=> y = 1000/15
=> y = 200/3 km/hr
Train Speed = 300/7 km/hr
Car speed = 200/3 km/hr
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