This problem involves calculating the average speed of a train (Q) given information about another train (P) that starts simultaneously from the opposite station. We are given the speed of train P and the time each train takes to reach its destination *after* passing each other.
For two trains starting at the same time from points A and B towards each other, if they meet at point C, and after meeting, train 1 takes time '\(t_1\)' to reach B and train 2 takes time '\(t_2\)' to reach A, then the ratio of their speeds is given by:
\(\frac{\text{Speed of Train 1}}{\text{Speed of Train 2}} = \sqrt{\frac{\text{Time taken by Train 2}}{\text{Time taken by Train 1}}}\)
In our case:
Using the formula:
\(\frac{S_P}{S_Q} = \sqrt{\frac{T_{Q_{after}}}{T_{P_{after}}}}\)
\(\frac{60 \text{ km/h}}{S_Q} = \sqrt{\frac{1 \text{ hour}}{4 \text{ hours}}}\)
\(\frac{60}{S_Q} = \sqrt{\frac{1}{4}}\)
\(\frac{60}{S_Q} = \frac{1}{2}\)
Cross-multiply to find '\(S_Q\)':
\(S_Q = 60 \times 2\)
\(S_Q = 120 \text{ km/h}\)
Therefore, the average speed of train Q is 120 km/h.
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