Math, asked by hitarthbhansali18, 9 months ago

A boat takes 5 hours to travel 12 km downstream and 16 km upstream, and it takes 7
hours to travel 16 km downstream and 24 km upstream. Find the speed of the boat in still
water and the speed of the stream.

Answers

Answered by AaryaThakur
4

Answer:

Let speed of boat be x and stream be y

Speed of boat in upstream = x-y

Speed of boat in downstream = x+y...............due to gravity.

time= dist/speed.

According to 1st condition;

12/x+y + 16/x-y = 5

According to 2nd condition;

16/x+y + 24/x-y = 7

Substitute 1/x+y = a and 1/x-y = b

12a + 16b = 5...............1

16a + 24b = 7................2

multiply eq 1 by 4 and eq 2 by 3

48a + 64b = 20..................3

48a + 72b = 21....................4

Substract eq 3 from 4

48a + 72b = 21

- 48a + 64b = 20

(-) (-) (-)

8b = 1 .............................eliminating 48a

b = 1/8

substitute b = 1/8 in eq 1

12a + 16 (1/8) = 5

12a + 2 = 5

12a = 5-2

12a = 3

a = 3/12

a = 1/4

Resubstitute a = 1/x+y and b = 1/ x-y

x+y=4 and x-y=8........................Both are DENOMINATORS

Add x+y = 4 and x-y = 8

x+y=4

x-y=8

2x = 12

x = 6

Substitute x = 6 in x+y= 4

6 + y = 4

y = 4-6

y = -2

Therefore,

Speed of boat is 6km/hr and

Speed of stream is -2km/hr.

I hope it helps!!!

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