Question

A boat covers 32 km upstream and 28 km downstream in 7 hours. It can
travel 21 km upstream and return in 5 hours. Find the speed of the boat in
still water and the speed of the stream.


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Answer 1

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Answer:

Let the speed of the boat in still water be x km/h and speed of the stream is y km/h.

Therefore, speed of the boat while upstream is (x−y) km/h and speed of the boat while downstream is (x+y) km/h

As we know that speed=

time

distance

, therefore, time=

speed

distance

It is given that the motor boat can travel 30 km upstream and 28 km downstream in 7 hours and also it can travel 21 km upstream and return in 5 hours, thus,

x+y

30

+

x−y

28

=7.............(1)

x+y

21

+

x−y

21

=5.............(2)

Let

x+y

1

=u and

x−y

1

=v, then the equations (1) and (2) becomes:

30u+28v=7..........(3)

21u+21v=5..........(4)

Multiplying equation (3) by 21 and equation (4) by 30 we get,

630u+588v=147..........(5)

630u+630v=150..........(6)

Now subtracting equation (5) from equation (6), we get

42v=3

⇒v=

14

1

Substitute the value of v in equation (4) then, u=

6

1

Since

x+y

1

=u and

x−y

1

=v, therefore,

x+y=6..........(7)

x−y=14..........(8)

Adding equations (7) and (8), we get:

2x=20

⇒x=10

Hence, the speed of the boat in still water is 10 km/h.