Downstream and Upstream

Algebra Level 2

The speed of the boat on still water is 8 km/hr. It can go a total of 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream (in km/hr).


The answer is 3.

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Sonakshi Gupta by Sonakshi Gupta , 21, India

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4 solutions

Adrian Delgado
Jan 2, 2015

Let speed of stream be v km/h Then the upstream spped is (8-v) km/h and the downstream speed is (8+v) km/h

Then we have the following equation:

15 8 − v + 22 8 + v = 5 15 ( 8 + v ) + 22 ( 8 − v ) = 5 ( 8 + v ) ( 8 − v ) 120 + 15 v + 176 − 22 v = 5 ( 64 − v 2 ) 120 + 15 v + 176 − 22 v = 320 − 5 v 2 5 v 2 − 7 v − 24 = 0 ( 5 v + 8 ) ( v − 3 ) = 0 \dfrac{15}{8-v} + \dfrac{22}{8+v} =5 \\ 15(8+v) + 22(8-v) = 5(8+v)(8-v) \\ 120 +15v +176 - 22v = 5(64-v^2)\\ 120+15v+176 -22v=320 - 5v^2 \\ 5v^2 - 7v -24 = 0 \\ (5v+8)(v-3)=0

The solutions of this equation are 3 and -8/5. Therefore the speed of strem is 3 km/h

6 Helpful 1 Interesting 1 Brilliant 0 Confused

The written equation is missing a semi-colon between the up stream and down stream.

Rob Janes - 4 years, 12 months ago

Disambut I wanderers it 3.5 and I can't so I fried 2 and 1 and wrong F * man

Dzaki Hakim - 4 years, 11 months ago

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I mean I tried

Dzaki Hakim - 4 years, 11 months ago
Sunil Pradhan
Dec 25, 2014

let speed of stream be x km/hr upstream speed = (8 + x) km/hr and

downstream speed = (8 – x) km/hr.

Total time = 15/(8 + x) + 22/(8 – x) = 5

15(8 – x) + 22/(8 + x) = 5(8 + x)(8 – x)

5x² – 7x + 24 = 0 then (x – 3)(5x + 8) = 0 taking + ve value x = 3 km/hr

3 Helpful 0 Interesting 0 Brilliant 0 Confused

This is the opposite of what 'upstream' and 'downstream' mean.

Michael Stevenson - 6 years, 5 months ago

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Still getting a correct answer....

Aman Kumar - 6 years, 5 months ago

I simply used logic to answer this type of question instead of using mathematics.I divided 15 (total km upstream in 5 hrs). so I divide 15 by 5 which is equal to 3

0 Helpful 1 Interesting 0 Brilliant 0 Confused

That is, sadly, not the value that was asked. It's just a coincident that it's the same number. What was asked is the speed of the stream, while 15/5 is the average upstream speed of the boat over the 5-hour journey, which isn't even going upstream for the full 5 hours.

Pascal Huppert - 7 months, 3 weeks ago

Also, that's still mathematics :)

Pascal Huppert - 7 months, 3 weeks ago
Madhav Srirangan
Dec 25, 2014

let speed of stream be x upstream speed=8+x downstream speed=8-x --->8+x=15/t1--->t1=15/8+x-----------(1) 8-x=22/t2--->t2=22/8-x------------------(2) t1+t2=5 add (1) and (2) to get eq 5x^2+7x-24=0 factorize :-) :-D :)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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