Question

A motor boat traveling at 15 km per hour in standing water, 30km in the direction of flow of water, will take 4 hours and 30 minutes to return, so what is the speed of the water?
a)4
b)5
c)6
d)10​

Answer 1

Answer:

Let the speed of the stream be x km/hr .

Speed downstream = (15 + x) km/hr.

Speed upstream = (15 - x) km/hr.

Time taken by the boat to go 30 km upstream =

$\frac{30}{15 - x} \: hours$

Time taken by the boat to return to 30 km downstream =

$\frac{30}{15 + x} \: hours$

It is given that the boat returns to the same point in 4 hrs and 30 min.

$\frac{30}{15 - x} + \frac{30}{15 + x} = \frac{9}{2} \\ \\ \frac{30(15 + x) + 30(15 - x)}{(15 + x)(15 - x)} = \frac{9}{2} \\ \\ \frac{450 + 450 - 30x + 30x}{225 - {x}^{2} } = \frac{9}{2} \\ \\ \frac{900}{225 - {x}^{2} } = \frac{9}{2} \\ \\ 9(225 - {x}^{2} ) = 1800 \\ \\ 225 - {x}^{2} = 200 \\ \\ {x}^{2} = 25 \\ \\ x = 5$

Hence the speed of stream is 5 km/hr.

Mark it as brainliest.