A person walks from point P to Q at 5 km/hr and returns from Q to P along the same route jogging at 10 km/hr. If the total time taken is 3 hours, what is the distance between P and Q?
10 km
Let the distance between P and Q be \(d\) km.
Time is distance divided by speed. Going P to Q at 5 km/hr takes \(\frac{d}{5}\) hours, and returning Q to P at 10 km/hr takes \(\frac{d}{10}\) hours.
The total time is given as 3 hours, so \(\frac{d}{5} + \frac{d}{10} = 3\).
Take the LCM of the denominators (10): \(\frac{2d}{10} + \frac{d}{10} = \frac{3d}{10} = 3\).
Solve for \(d\): \(3d = 30 \Rightarrow d = 10\) km.
Check: at 5 km/hr, 10 km takes 2 hours; at 10 km/hr, 10 km takes 1 hour; total \(2 + 1 = 3\) hours, as required.
Hence, the distance between P and Q is 10 km.
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