Question

A motorboat goes downstream in a river and covers the distance between two coastal towns in 5 hrs and it covers the distance upstream in 6hrs.If the speed of water is 4km/hr. Find the distance between two towns.

Answer 1

Hint:Substitute the values given, in the formula of speed in terms of distance and time but here we have to consider speed in both upstream and downstream. The upstream speed is taken as the difference between the speed of the boat and the speed of the water. The downstream speed is taken as the sum of the speed of the boat and speed of water
Upstream speed = x – y
here x = speed of the boat
and y = speed of the water
here we take the difference between the speeds because the boat travels opposite to the flow of the water.
Downstream speed = x + y
here we take some of the speeds because the boat travels along the flow of the water
we know that $speed = \dfrac{{dis\tan ce}}{{time}}$
=> distance = speed × time

Complete step by step answer:
From the given question
It is known that the time taken to cover distance between the coastal towns by upstream is 6km/hr and by downstream is 5km/hr.
speed of the water is (y) = 4km/hr,
Let the distance between two coastal towns be d
case1: through upstream speed
d = (x-4) × 6 --(1)
case2: through downstream speed
d = (x+4) × 5 --(2)
from equation (1) and (2) , as d is same in both the cases, we get
(x-4) × 6 = (x+4) × 5
6x – 24 = 5x + 20
6x - 5x = 20 + 24
x = 44
from equation (1)
d = (44-4) × 6= 40 × 6 = 240

Note:
 Do not make calculation mistakes. Make sure to read the question clearly whether the given information is related to upstream or downstream. Go through the river and boat concepts once again. And the distance given may not be always equal to each other so make sure to read the question properly.