Given:
Total distance = 60 km
Upstream time = 5 hours
Downstream time = 3 hours
Find-:
The rate of boat in still water.
Explanation-:
Let
The speed of the boat in still water is"x"
The speed of the water is "y"
For upstream ( Against the current )
Speed of boat is:
[tex]=x-y[/tex][tex]\begin{gathered} \text{ Distance }=60\text{ km} \\ \\ \text{ Time }=5\text{ hours} \end{gathered}[/tex]Use the formula:
[tex]\text{ Speed}=\frac{\text{ Distance}}{\text{ Time}}[/tex]For upstream speed is:
[tex]\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x-y=\frac{60}{5} \\ \\ x-y=12..............(1) \end{gathered}[/tex]For downstream,
[tex]\text{ Speed}=x+y[/tex][tex]\begin{gathered} \text{ Distance}=60\text{ km} \\ \\ \text{ Time}=3\text{ hours} \end{gathered}[/tex]Use the formula of distance
[tex]\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x+y=\frac{60}{3} \\ \\ x+y=20 \\ \\ y=20-x................(2) \end{gathered}[/tex]From eq(2) put the value of "y" in eq(1) then the value is:
[tex]\begin{gathered} x-y=12...........(1) \\ \\ y=20-x...............(2) \end{gathered}[/tex][tex]\begin{gathered} x-y=12 \\ \\ x-(20-x)=12 \\ \\ x-20+x=12 \\ \\ 2x-20=12 \\ \\ 2x=12+20 \\ \\ 2x=32 \\ \\ x=\frac{32}{2} \\ \\ x=16 \end{gathered}[/tex]The rate of the boat in still water is 16 km/hour