Question

Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours<br />
if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels<br />
200 km by train and rest by car. Find the speed of the train and the car

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation:

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.