SOLUTION: a cyclist travels 30mi in 3 hours going against the wind and 80mi in 5 hours with wind. What is the rate of the cyclist in still air and what is the rate of the wind?

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Question 275984: a cyclist travels 30mi in 3 hours going against the wind and 80mi in 5 hours with wind. What is the rate of the cyclist in still air and what is the rate of the wind?
Found 5 solutions by mananth, richwmiller, ikleyn, timofer, greenestamps:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
cyclist travels 30mi in 3 hours going against the wind and 80mi in 5 hours with wind. What is the rate of the cyclist in still air and what is the rate of the wind?
let speed of wind be x
let cycle rate in still air be y
Distance / rate = time
30 /y-x = 3
or y-x=10
AND
80 / x+y= 5
or
x+y = 80/5
x+y= 16

y-x=10
x+y=16
therefore 2y= 26
y=13 mph
x=3 mph

Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website!
3*(c-w)=30
5*(c+w)=80
c-w=10
c+w=16
2c=26
c=13
w=3

Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website!
.
a cyclist travels 30mi in 3 hours going against the wind and 80mi in 5 hours with wind.
What is the rate of the cyclist in still air and what is the rate of the wind?
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The solution in the post by @mananth is incorrect and makes no sense.

The fact that the rate of the cyclist is 'x' miles per hour at no wind and the fact
that the rate of the wind is 'y' miles per hour DO NOT IMPLY that the effective rate
of the cyclist with the wind is (x+y) mph and the effective rate of the cyclist against
the wind is (x-y) miles per hour.

Only a person absolutely illiterate in Physics could create/compose such a nonsense.

No one peer-reviewed Math textbook or Physics textbook would publish such a non-sensical
gibberish.

My advise to a reader is to ignore the problem itself as a kind of nonsense
and ignore the solution by @mananth since it is WRONG TEACHING.

The creator of this "problem" should be ashamed of himself for composing such nonsense
and distributing it on the Internet.

Answer by timofer(155)   (Show Source):
You can put this solution on YOUR website!
The stated problem does not make much sense. How exactly wind speed affects a bicyclist on the ground is not clear.

Answer by greenestamps(13326)   (Show Source):
You can put this solution on YOUR website!

These kinds of problems are intended as mathematical exercises, without concern for the physics.

In this problem, the speed of the cyclist against the wind is 30/3 = 10 mph and with the wind is 80/5 = 16 mph.

You can solve the problem using formal algebra:
c the speed of the cyclist in still air
w the speed of the wind
c+w=16; c-w=10 --> c=13, w=3

But an informal solution using logical reasoning is much easier: the speed of the cyclist is halfway between his speed with the wind and his speed against the wind:
(10+16)/2 = 13
and the speed of the wind is the difference between that speed and either of the other speeds:
16-13 = 3 mph, or 13-10 = 3 mph

ANSWERS: cyclist 13 mph; wind 3 mph