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  4. A man swimming downstream overcome a float at a point M. After travelling distance D he turned back and passed the float at a distance of D/2 from the point M, then the ratio of speed of swimmer with respect to still water to the speed of the river will be

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Q. A man swimming downstream overcome a float at a point $M$. After travelling distance $D$ he turned back and passed the float at a distance of $D/2$ from the point $M$, then the ratio of speed of swimmer with respect to still water to the speed of the river will be

Motion in a Straight Line

Solution:

Time taken by man to go from $M$ to $P$ and then $P$ to $N =$ time taken by float to go from $M$ to $N$.
image
$\frac{D}{v+u}+ \frac{D}{2(v-u)} = \frac{D}{2u}$
Simplify to get $\frac{v}{u} = 3$.