Question

A boat goes up-stream $30$ km and down-stream $44$ km in $10$ hrs. It also goes up-stream $40$ km and down-stream $55$ km in $13$ hrs. Find the speed of the stream and the boat

Answer 1

Let the speed of the boat be $x$ and speed of the stream be $y$.

Then speed of the boat in upstream $=(x-y)$ kmph

Speed of the boat in downstream $=(x+y)$ kmph

Then, $\frac{30}{x-y}+\frac{44}{x+y}=10$ ....(1)

and $\frac{40}{x-y}+\frac{55}{x+y}=13$ ....(2)

Let $\frac{1}{x-y}=a$ and $\frac{1}{x+y}=b$

Thus, $30a+44b=10$ ....(3)

and $40a+55b=13$ ....(4)

Solving both the equations, we get $x=8$.

Putting this value in any of the equations, we get $y=3$.

Hence, speed of boat is $8$ kmph and speed of the stream is $3$ kmph.