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.
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Answered by
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
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
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
⠀
∴ Speed of the Stream will be 8 km/hr.
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