Question

A motor boat whose speed in still water is $10$ km/h went $91$ km downstream and then returned. Calculate the speed of the river flow, if the trip took $20$ hours.

Answer 1

$speed=\frac{distance}{time}⟹time=\frac{distance}{speed}$

total time $=$timeof assent $+$time of desent

let speed of flow $=\text{x}$

speed in ascent$=$speed of boat in still water $+$ speed of water flow

speed in decent$=$speed of boat in still water $-$ speed of water flow

time of ascent$=\frac{91}{10+\text{x}}$

time of decent$=\frac{91}{10-\text{x}}$

$20=\frac{91}{10+\text{x}}+\frac{91}{10-\text{x}}$

$20\times (10+\text{x})(10-\text{x})=91(10+\text{x})+91(10-\text{x})$

$2000-20{\text{x}}^2=1820$

${\text{x}}^2+91-100=0$

$x^2=9$

$x=3$

Speed of flow = 3km/h