Question

A sailor goes 8 km down stream in 40 minutes and returns in 1 hour. Determine the speed of the sailor in still water and the speed of the current.

Standard:- 10

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Answer 1

Hey

Here is your answer,

Let speed of stream = y kmph & speed of boat = x kmph

speed downstram((x + y)kmph) = 8 * 60 / 40 kmph
= 12 kmph

speed upstream((x - y) kmph) = 8/1 kmph
= 8 kmph

x + y = 12
x - y = 8
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2x = 20,
2y = 4

x = 10,
y = 2

=>Speed of stream = 2 kmph,
Speed of boat = 10 kmph

Hope it helps you!

Answer 2

HELLO !!!.....


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Let the speed of the sailer in still water be x km/hr.
The speed of the current be y km/hr.

Speed upstream = (x-y) km/hr
Speed downstream = (x+y) km/hr

Now, time taken to cover 8 km downstream = 8/ x+y hrs.
Time taken to cover 8 km upstream = 8/x-y hrs.

●But, time taken to cover 8 km downstream in 40 minutes or 40/60 hrs that is 2/3 hours.

$\frac{8}{x + y} = \frac{2}{3} \\ \\ 8 \times 3 = 2(x + y) \\ \\ 24 = x + y$


Dividing both sides by common factor 2 we get

12 = x + y - - - - - (1)


●Time taken to cover 8km upstream in 1 hour

$\frac{8}{x - y} = 1 \\ \\ 8 = 1(x - y) \\ \\ 8 = x - y \: \: \: - - - - - - - (2)$


●By solving these equation (1) and (2) we get

x + y = 12

x - y = 8
__________
2x = 20

==> x = 10

●Substitute x+10 in equation (1) we get

x + y = 12
10 + y = 12
y = 12 - 10
==> y = 2


●Hence, the speed of sailor is 10 km/hr.

●The speed of current is 2 km/hr.


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Hope it helps u !!!

# Nikky