Question

A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in $6\frac{1}{2}$ hours. What is the speed of the current ?

• A. 1 km/hr
• B. 2 km/hr
• C. 1.5 km/hr
• D. 2.5 km/hr

Answer 1

The correct option is B 2 km/hr

We take the speed of the boat$=x$ km/hr. and that of the water current$=y$ km/hr.

In the first case, their relative speed$=x-y$ upstream & $x+y$ downstream..

UPSTREAM-

The distance$=24$km.

So the time taken=$\frac{24}{x-y}$.

DOWNSTREAM-

The distance$=36$km.

So the time taken=$\frac{36}{x+y}$.

$\therefore$ the total time taken

=$\frac{24}{x-y}+\frac{36}{x+y}=6$(given).

Let $x-y=a$ & $x+y=b$.

Then the above equation becomes,

$24a+36b=6$

Or $4a+6b=1$.........(i).

In the second case, their relative speed$=x-y$ upstream & $x+y$ downstream..

UPSTREAM-

The distance$=36$km.

So the time taken=$\frac{36}{x-y}$.

DOWNSTREAM-

The distance$=24$km.

So the time taken=$\frac{24}{x+y}$.

$\therefore$ the total time taken

=$\frac{36}{x-y}+\frac{24}{x+y}=6\frac{1}{2}hr.=\frac{13}{2}hr$(given).

Now we have assumed that $x-y=a$ & $x+y=b$.

Then the above equation becomes

$36a+24b=$$\frac{13}{2}$

Or $72a+48b=13$.........(ii).

$\left(ii\right)-\left(iii\right)⟶60b=5$

Or $b=\frac{1}{12}$

Or $x+y=12$.........(iv).

Putting b=$\frac{1}{12}$ in (i),

$4a+6\times \frac{1}{12}$= 1

Or $a=\frac{1}{8}$

Or $x-y=8$........(v).

Subtracting (iv) from (v),

$2y=4$

Or $y=2$km/hr.

So the speed of the current$=2$km/hr.