Question

a motorboat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in four and a half hours. the speed of the stream is:

Answer 1

The speed of the stream is 5km/hr

Answer 2

Let the speed of the stream be x km/h

$\therefore$ Speed Downstream = (15+x) km/h

Speed upstream = (15-x)km/h

Time taken to travel 30 km downstream = $\sf{\frac{30}{15+x}h}$

Time taken to travel 30 km upstream = $\sf{\frac{30}{15-x}h}$

Given, total time taken =

$\sf\green{4 \: hours \: 30 \: mins. = (4 + \frac{1}{2} )h = \frac{9}{2} h}$

$\longrightarrow$$\sf\red{ \frac{30}{15 + x} + \frac{30}{15 - x} = \frac{9}{2}}$

$\longrightarrow$$\sf\red{\frac{10}{15 + x} + \frac{10}{15 - x} = \frac{3}{2} }$

$\longrightarrow$$\sf\red{\frac{10(15 - x + 15 + x)}{(15 + x)(15 - x)} = \frac{3}{2} }$

$\longrightarrow$$\sf\red{10 \times 30 \times 2 = 3(225 - {x}^{2} )}$

$\longrightarrow$$\sf\red{200 = 225 \times {x}^{2}}$

$\longrightarrow$$\sf\red{{x}^{2} = 25 \: or \: x = ±5}$

As speed cannot be negative, x ≠-5, so x = 5

Hence, the speed of the stream = 5km/h