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 motor boat speed in downstream = (u – v) km/h
Motorboat has taken time to travel 30 km upstream
t1=30u−vh
and motorboat has taken time to travel 28 km downstream,
t1=30u−vh
and motor boat has taken time to travel 28 km downstream
t2=28u+vh
by first condition, a motor boat can travel 30 km upstream and 28 km down stream in 7 h
i.e., t1+t2 = 7h
⇒30u−v+287+v=7
Now, motor boat has taken time to travel 21 km upstream and return i.e., t3=21u−v (upstream)
(for downstream)
And t4=21u−v
By second condition, t4=t3=5h
⇒21u−v+21u−v=5
Let x=21u−v and y=21u−v
Eqs. (i) and (ii) becomes 30x + 28y = 7
and 21x + 21y = 5
⇒ x+y=521
Now, multiplying in Eq. (iv) by 28 and then subtracting from Eq. (iii), we get
30x + 28y = 7
28x + 28y = 14021
2x=7−203=21−203
2x=13⇒x=16
On putting the value of x in Eq, (iv), we get
16+y=521
⇒y=521−16=10−742=342⇒114
∴x=1u+v=16⇒u+v=6
And y=1u+v=114
⇒ u−v=14
Now, adding Eqs. (v) and (vi), we get
2u = 20 ⇒ u = 10
On putting the value of u in Eq (v), we get
10 + v = 6
⇒ v = - 4
Hence, the speed of the motorboat in still water is 10 km/h and the speed of the stream 4 km/h