Question

A boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is ___ km/hr. Type your answer below!

Answer 1

Question

A boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is ___ km/hr.

Answer

$\mathtt{Let \: the \: speed \: of \: the \: stream \: be \: x \: km/hr}$

$\mathfrak{Now,}$

$\mathfrak{Speed~Downstream=(15+x)km/hr}$

$\mathfrak{Speed~Upstream=(15-x)km/hr}$

$\mathfrak{According~to~the~question}$

$\leadsto\mathfrak{\frac{30}{15 + x} + \frac{30}{15 - x} = 4 \frac{1}{2}}$

$\leadsto\mathfrak{\frac{30(15+x)+30(15-x)}{(15)²-x²}=\frac{9}{2}}$

$\leadsto \mathfrak{\frac{450-30x+450+30x}{225-x²}=\frac{9}{2}}$

$\leadsto\mathfrak{\frac{900}{225-x²}=\frac{9}{2}}$

$\leadsto\mathfrak{1800=2025-9x²}$

$\leadsto \mathfrak{9x²=225}$

$\leadsto\mathfrak{x²=\frac{225}{9}}$

$\leadsto \mathfrak{x²=25}$

$\leadsto \mathfrak{x=5}$

$\mathtt{Hence~,Speed~is~5km/hr}$