Question

A rescue boat takes 12 hours to row 90 km downstream and 70 km upstream. what is the rate of current if the boat take 9 hours to row 72 km downstream

Answer 1

$90 \div 12$
$\times 70$

Answer 2

We will assume the speed of the boat as B and the Speed of current as C

speed of downstream = (B + C) Km/h

speed of upstream = (B - C) Km/h

We are given,

time = distance /speed

so, time taken in downstream + time taken in upstream = 12 h

90/(B + C) + 70/(B - C) = 12 ----(1)

Time taken in downstream = 9 h

72/(B + C) = 9

B + C = 8 km/h---------(2) , put it in equation (1)

90/8 + 70/(B -C) = 12

45/4 + 70/(B - C) = 12

70/(B - C) = 12 - 45/4 = 3/4

B - C = 280/3 km/h -------(3)

Now we will solve both equations (2) and (3),

2B = 280/3 + 8 => B = 140/3 + 4 = 152/3 km/h

now we will Put B in equation (2) ,

C = 8 - 152/3 = (24-152)/3 = -128/3 km/h

here , negative sign shows that Current is just opposite side of our assumption

So speed of current = -128/3 km/h