Question

A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car. [

Answer 1

Total distance a man has to be covered
= 600 Kms
Man covered distance by train = 400 Kms
Therefore, the distance covered by car
= 600 - 400
= 200 Kms
Total time taken for full journey = 6 hrs 30 min
= 6 (1 / 2)
= 13 / 2 hours.
FORMULA :
Speed = distance / time
distance / speed = time
CASE 1.
Let the speed of train = X km/ h
And speed of car = Y Km/h
Therefore,
(400 / X) + (200 / Y) = 16 / 2
Lcm = XY
400Y + 200X = 16XY / 2
800Y + 400X = 16XY
Divide it by 4.
200X + 100 Y = 4XY__________(1)

CASE 2.
Man covered distance by train = 200 Kms
Therefore, the distance covered by car
= 600 - 200
= 400 Kms
Total time taken for full journey = 7 hrs
Let the speed of train = X km/ h
And speed of car = Y Km/h
Therefore,
(200 / X) + (400 / Y) = 7
Lcm = XY
200Y + 400X = 7XY__________(2)
Subtract (1) from (2)
(200 - 200)X + (400 - 100)Y = (7 - 4)XY
300Y = 3XY
100 = X
Speed of train is 100 Kms/ h
Subsitute X value in (2)
200Y + (400 x 100) = 7(100)Y
40000 = (700 - 200)Y
40000 = 500Y
Y = 40000 / 500
Y = 80
Therefore, speed of car is 80 Kms / h.

Answer 2

Answer:

Refers to the attachment