Question 65

A man covers a certain distance on a toy train. If the train moved 4 km/hr faster, it would take 30 minutes less. If it moved 2 km/hr slower, it would have taken 20 minutes more, What is the distance covered?

Solution

Let the time taken to cover 'D' km with speed S km/h is T hours.

D = ST

$$D = (S + 4) * (T - \frac{30}{60})$$

$$D = ST - \frac{S}{2} + 4T - \frac{4}{2}$$

$$D = D - \frac{S}{2} + 4T - \frac{4}{2}$$

8T - S = 4 ......... (1)

$$D = (S - 2) * (T + \frac{20}{60})$$

$$D = ST + \frac{S}{3} - 2T - \frac{2}{3}$$

$$D = D + \frac{S}{3} - 2T - \frac{2}{3}$$

S - 6T = 2 ......... (2)

From (1) and (2):

T = 3 and S = 20

D = ST = 60 km

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