A motorboat can travel 30 km upstream and 28 km downstream in 7 h. It can travel 21 km upstream and return in 5 h. Find the speed of the boat in still water and the speed of the stream.

Question

Philoid · Accepted Answer

Let the speed of the motorboat in still water and the speed of the stream are u km/h and v km/h, respectively.

Then, a motorboat speed in downstream

and a motorboat speed in upstream

Motorboat has taken time to travel 30 km upstream,

and motorboat has taken time to travel 28 km downstream,

By first condition, a motorboat can travel 30 km upstream and 38 km downstream in 7 h i.e.,

…(i)

Now, motorboat has taken time to travel 21 km upstream and return i.e., [for upstream]

and [for downstream]

By second condition,

…(ii)

Let

Eqs. (i) and (ii) becomes …(iii)

and

…(iv)

Now, multiplying in Eq. (iv) by 28 and then subtracting from Eq. (iii), we get

On putting the value of x in Eq. (iv), we get

…(v)

and
…(vi)

Now, adding Eqs. (v) and (vi), we get

2u = 20

So u = 10

On putting the value of in Eq. (v), we get

10 + v = 6

So v = - 4

Hence, the speed of the motorboat in still water is 10 km/h and the speed of the stream 4 km/h.