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.


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