Question

A boat takes 8 hours to travel 30 km upstream and 36 km downstream; but it takes 10 hours to travel 36

km upstream and 48 km downstream. Find the speed of the boat in still water and the speed of the

stream.


Select one:

A. 9 km/hr and 3 km/hr

B. 10 km/hr and 2 km/ hr

C. 8 km/hr and 3 km/hr   

D. 10 km/hr and 3 km/hr

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Answer 1

hope this helps you

this is one of the most important. question and it always comes in exams in either 3 marker or 5 marker or sometimes even both.

you should practice it thoroughly

Answer 2

Answer:

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Option (b) is correct

Let speed of the boat =x km/h

and speed of stream =y km/h

Speed upstream = speed of boat - speed of stream

i.e. x-y

speed downstream = speed of boat + speed of stream

i.e x+y

GIVEN

$\frac{36}{x + y} + \frac{24}{x - y} = 6hrs$

$\frac{48}{x + y} + \frac{40}{x - y} = 9hrs$

Multiply eq (1) by 5 and eq (2) by 3

$\frac{180}{x + y} + \frac{120}{x - y} = 30 - - - - (3)$

$\frac{144}{x + y} + \frac{120}{x - y} = 27 - - - (4)$

Subtract eq (3) and eq (4)

$\frac{36}{x + y} = 3 \\ x + y = 12 - - - - (5)$

Put value in eq (4)

$\frac{144}{12} + \frac{120}{x - y} = 27 \\ x - y = 8 - - - (6)$

Add (5) and (6)

$x + y + x - y = 20 \\ 2x = 20 \\ x = 10km/h$

and put value of x in (6)

10-y=8

$y = 2km/h$

Speed of boat in still water =10km/h

Speed of stream =2 km/h