Question

A boat can travel 28 km downstream and 20 km upstream in 7 hrs. Also, this boat can travel 21 km downstream and 18km upstream in 6 hoirs. What is the speed of the boat in still water and the speed of the stream?

Answer 1

Hi,

$$\begin{gathered} letthespeedofboat=xandspeedofriver=y \\ upstreamspeed=x-y \\ dounstreamspeed=x+y \\ so \\ 7=\frac{28}{x+y}+\frac{20}{x-y}....\left(1\right) \\ 6=\frac{21}{x+y}+\frac{18}{x-y}...\left(2\right) \\ nowlet\frac{1}{x+y}=uand\frac{1}{x-y}=v \\ 28u+20v=7 \\ 7u+5v=\frac{7}{4}.....\left(3\right) \\ 21u+18v=6 \\ 7u+6v=2....\left(4\right) \\ subtractequation3-4 \\ -v=\frac{-1}{4} \\ v=\frac{1}{4}=\frac{1}{x-y} \\ sox-y=4....\left(5\right) \\ puttingvalueofvinequation4 \\ 7u=2-6\times \frac{1}{4}=\frac{1}{2} \\ u=\frac{1}{14}=\frac{1}{x+y} \\ sox+y=14......\left(6\right) \\ addequation5and6 \\ 2x=18 \\ x=9kmph \\ soy=5kmph \end{gathered}$$
​Regards