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Question 8
A motor boat 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.

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Solution

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=30uvh
and motorboat has taken time to travel 28 km downstream,
t1=30uvh
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
30uv+287+v=7
Now, motor boat has taken time to travel 21 km upstream and return i.e., t3=21uv (upstream)

(for downstream)
And t4=21uv

By second condition, t4=t3=5h
21uv+21uv=5
Let x=21uv and y=21uv
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=7203=21203
2x=13x=16
On putting the value of x in Eq, (iv), we get
16+y=521
y=52116=10742=342114
x=1u+v=16u+v=6
And y=1u+v=114
uv=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


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