Step 1 : Formulation : We know the speed of the river and the time taken to cover the distance between two places. We have to find the speed of the boat in still water.
Mathematical Description : Let us write x for the speed of the boat, t for the time taken and y for the distance travelled. Then y = tx ....(1)
Let d be the distance between the two places. While going upstream.
The actual speed of boat = speed of the boat - speed of the river
∴ The boat is travelling against the flow of the river.
So, the speed of the boat in upstream = (x - 4)km/h.
It takes 8hours to cover the distance between the towns upstream. So from (1), we have
d = 8(x + 4) ....(2)
When going downstream,
The speed of the boat in downstream = (x + 4)km/h
The boat takes five hours to cover the same distance downstream, so
d = 5(x + 4) .....(3)
From (2) and (3), we have
5(x + 4) = 8(x - 4)
Step 2. Finding the solution.
Solving for a in equation (4), we get x = 52/2
Step 3. Interpretation.
Since x = 52/3 , therefore the speed of the motorboat in still water is 52/3km/h.
We have assumed that
The speed of the river and the boat *** constant all the time.
The effect of the friction between the boat and water and the friction due to air is negligible.
Step 4. Validation of result :
The speed of the motor boat is 52/3km/h and the distance between two towns,
=> y = 106.66km.
Hence the distance between two towns = 106.66km.
