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.

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$200 k m$

$245 k m$

$260 k m$

$240 k m$

answer is C.

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Detailed Solution

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 $s p e e d = \frac{d i s \tan c e}{t i m e}$
distance = speed × time

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