Math, asked by zoyaranblachas, 1 year ago

A motor boat , whose speed is 24 km/h in still water, takes 1 hr more to go 32 km upstream than to return downstream to the same spot, find the speed of the stream.

Answers

Answered by Faisal07
4
let c = the rate of the stream current
then
(24+c) = the effective speed of the boat downstream
and
(24-c) = the effective speed up stream

Write a time equation; time = dist/rate

Time up - time down = 1 hr

{32/(24-c)}-
{32/(24+c)}=1

Multiply by (24-c)(24+c)

then we get an equation as:

32(24+c) - 32(24-c) = (24-c)(24+c)
768 + 32c - 768 + 32c = 576 + 24c - 24c - c^2

Combine like terms
64c = 576 - c^2
Arrange as a quadratic equation

c^2+64c-576=0

You can use the quadratic formula a=1, b=64, c=-576, but this will factor to:
(x+72)(x-8)=0

since we want only positive part we get x=8

so the speed of the stream is 8km/h


Answered by Anonymous
3

Answer:

Let the speed of stream be x.

Then,

Speed of boat in upstream is 24 ‒ x

In downstream, speed of boat is 24 + x

According to question,

Time taken in the upstream journey ‒ Time taken in the downstream journey = 1 hour

\implies\tt \dfrac{32}{24 - x} - \dfrac{32}{24 + x} = 1 \\\\\\\implies\tt\dfrac{24 + x - 24 + x}{{24}^{2} -{x}^{2}} = \dfrac{1}{32} \\\\\\\implies\tt \dfrac{2x}{576 -{x}^{2}} = \dfrac{1}{32}\\\\\\\implies\tt 2x \times 32 = 576 -{x}^{2}\\\\\\\implies\tt {x}^{2} + 64x - 576 = 0\\\\\\\implies\tt {x}^{2} + 72x - 8x - 576 = 0\\\\\\\implies\tt x(x + 72) - 8(x + 72) = 0\\\\\\\implies\tt (x - 8)(x + 72) = 0\\\\\\\implies\tt \green{x = 8} \quad or \quad \red{x =- 72}

Speed of the Stream will be 8 km/hr.

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