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
