Question

A’ can swim 54 km downstream in 4.5 hours while B can swim 27 km in upstream in 5.4 hours. if the speed of A in still water is 3 times that of the speed of the stream, then find the total time taken by A to cover 21 km in upstream and time taken by B to cover 55 km in downstream (speed of stream is same for A and B).
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Answer 1

Have a nice day dear officer

Answer 2

Given,

A can swim 54 km downstream in 4.5 hours while B can swim 27 km upstream in 5.4 hours. if the speed of A in still water is 3 times that of the speed of the stream.

To find,

The total time taken by A to cover 21 km upstream and the time taken by B to cover 55 km downstream.

Solution,

Let the speed of the stream is s and the speed of the person is u.

The downstream speed of A is,

$u+s=\frac{54}{4.5}\\=\frac{54 \times 10}{45} \\\\=12 kmph...(1)$

The upstream speed of B is,

$u-s=\frac{27}{5.4}\\=\frac{27 \times10}{54}\\ \\=5 kmph...(2)$

Solve equations (1) and (2) to find u and s.

$u+s=12...(1)\\u-s=5...(2)$

After adding equations (1) and (2),

$2u=17\\u=\frac{17}{2}$

and,

$\frac{17}{2}+ s=12\\s=12-\frac{17}{2}\\ =\frac{24-17}{2}\\ =\frac{7}{2}$

Let the speed of A in still water is $u_{A}$, the speed of B in still water be $u_{B}$ and the speed of stream for A and B is $\frac{7}{2}$.

The speed of A is still water is,

$u_{A}=3 \times \frac{7}{2}\\ =\frac{21}{2}$

The speed of B is still water is,

$u_{B}= \frac{17}{2}$

The time taken by A to cover 21 km upstream is,

$\frac{21}{\frac{21}{2}-\frac{7}{2}}=\frac{21}{\frac{14}{2}}\\\\=3 hours$

The time taken by B to cover 55 km downstream is,

$\frac{55}{\frac{17}{2}+\frac{7}{2}}=\frac{55}{\frac{24}{2} }\\ =\frac{55}{12} hours$

Thus, The time taken by A to cover 21 km upstream is 3 hours, and the time taken by B to cover 55 km downstream is $\frac{55}{12}$.