A race consists of three tracks – an uphill track from A to B, a downhill track from B to C, and an uphill track from C to D. The lengths of the three tracks are equal. Anil travelled from A to D covering the uphill and downhill tracks at 6 km/hr and 9 km/hr respectively. He took hours to reach D. Find the time that he would take to return from D to A (in hrs).2
Question
A race consists of three tracks – an uphill track from A to B, a downhill track from B to C, and an uphill track from C to D. The lengths of the three tracks are equal. Anil travelled from A to D covering the uphill and downhill tracks at 6 km/hr and 9 km/hr respectively. He took hours to reach D. Find the time that he would take to return from D to A (in hrs).2
Solution
The problem is asking for the time it would take for Anil to return from D to A.
Given that the speeds on the uphill and downhill tracks are 6 km/hr and 9 km/hr respectively, and the total time taken to travel from A to D is 2 hours.
Let's denote the distance of each track as 'd'. So, the total distance from A to D is 3d.
The time taken to travel from A to B (uphill) is d/6, from B to C (downhill) is d/9, and from C to D (uphill) is d/6.
So, the total time taken from A to D is d/6 + d/9 + d/6 = 2 hours.
Solving this equation for 'd' gives d = 4.8 km.
Now, if Anil returns from D to A, he will travel downhill from D to C, uphill from C to B, and downhill from B to A.
The time taken to travel from D to C (downhill) is d/9, from C to B (uphill) is d/6, and from B to A (downhill) is d/9.
So, the total time taken to return from D to A is d/9 + d/6 + d/9 = 4.8/9 + 4.8/6 + 4.8/9 = 1.6 hours.
Therefore, Anil would take 1.6 hours to return from D to A.
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