A motorboat goes upstream on a river and covers the distance between two towns on the riverbank in 6 hours. It covers this distance downstream in 5 hours. If the speed of the stream is 1.5 km/h, find the speed of the boat in still water. [This problem is challenging.
If x is the speed, then since distance = speed*time,
6(x-1.5) = 5(x+1.5)
16.5
To solve this problem, we can use the concept of relative speed.
Let's assume the speed of the boat in still water is 'b' km/h.
When the boat goes upstream, it has to overcome the speed of the stream, so the effective speed is reduced by the speed of the stream. Therefore, the speed of the boat relative to the shore is (b - 1.5) km/h.
When the boat goes downstream, it gets assistance from the speed of the stream, so the effective speed is increased by the speed of the stream. Therefore, the speed of the boat relative to the shore is (b + 1.5) km/h.
We are given that the boat covers the distance between the two towns in 6 hours when going upstream, and in 5 hours when going downstream.
Using the formula Distance = Speed * Time, we can set up the following equations:
Distance upstream = (b - 1.5) * 6
Distance downstream = (b + 1.5) * 5
Since the distances in both directions are the same, we can set these two equations equal to each other:
(b - 1.5) * 6 = (b + 1.5) * 5
Simplifying this equation:
6b - 9 = 5b + 7.5
b = 16.5
Therefore, the speed of the boat in still water is 16.5 km/h.