The road connecting two towns, A and B, goes only uphill or downhill, i.e., there is no stretch of road that is level. Vijay’s car does a constant 40 kmph uphill and 80 kmph downhill. Find the distance between A and B, if it takes exactly nine hours for Vijay to make one round trip from A to B and back.
Question
The road connecting two towns, A and B, goes only uphill or downhill, i.e., there is no stretch of road that is level. Vijay’s car does a constant 40 kmph uphill and 80 kmph downhill. Find the distance between A and B, if it takes exactly nine hours for Vijay to make one round trip from A to B and back.
Solution
Let's denote the distance from town A to town B as D.
Since the road only goes uphill or downhill, we know that the distance from A to B is the same as the distance from B to A.
When Vijay is driving uphill from A to B, his speed is 40 kmph. Therefore, the time it takes him to drive from A to B is D/40 hours.
When Vijay is driving downhill from B to A, his speed is 80 kmph. Therefore, the time it takes him to drive from B to A is D/80 hours.
The total time for the round trip is the sum of the time it takes to go from A to B and the time it takes to go from B to A. According to the problem, this total time is 9 hours.
Therefore, we can set up the following equation to solve for D:
D/40 + D/80 = 9
To solve for D, we first need to find a common denominator for the fractions on the left side of the equation. The least common multiple of 40 and 80 is 80, so we multiply the first fraction by 2/2 to get:
2D/80 + D/80 = 9
This simplifies to:
3D/80 = 9
To solve for D, we multiply both sides of the equation by 80/3:
D = 9 * (80/3) = 240 km
Therefore, the distance between town A and town B is 240 km.
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