ii. Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours
if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels
200 km by train and rest by car. Find the speed of the train and the car
Answers
solution;
Case 1:
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Total distance = 600km
Distance covered by train: 120km
Time taken by train: (120)/x km/h [Let 'x' be the speed of the train]
Distance covered by car: (600-120) = 480km
Time taken by car: (480)/y km/h [Let 'y' be the speed of the car]
Total time taken: (120)/x + (480)/y = 8 or (10)/x + (40)/y = 2/3 or (30)/x + (120)/y = 2 ...... (1)
Case II:
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Total distance covered by train: 200 km
Total time taken by train: (200)/x km/h
Total distance covered by car: (600-200) = 400 km
Total time taken by car: (400)/y km/h
Total time taken: 8(20/60) = (25)/3
(200)/x + (400)/y = (25)/3
or (600)x + (1200)/y = 25 ..... (2)
Let 1/x be u and 1/y be v .... (3)
Equations are then:
600u + 1200v = 25
30u + 120v = 2
Multiplying equation (1) by 20 and subtracting the equations we get:
1200v = 15 ; v = (15)/(1200)
Since, 1/y = v
y = (1200)/3 = 80
y = 80 km/h
So, the speed of the car is 80 km/h.
Hence the speed of the train,
Multiplying equation (1) by 10 and subtracting equations we get:
300u = 5
u = 5/(300)
Since, 1/x = u
x = (300)/5 ; x = 60
x = 60 km/h
So, the speed of the train is 60 km/h.
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