SOLUTION: john is riding his bike at 15 km against the wind. it takes him 1 hour to complete is trip. if he travels the same distance with the wind and it takes him 36 minutes, what is the r

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Question 235676: john is riding his bike at 15 km against the wind. it takes him 1 hour to complete is trip. if he travels the same distance with the wind and it takes him 36 minutes, what is the rate of the wind?
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the rate with no wind. Then let represent the rate of the wind.

When he is riding into the wind, his rate relative to the ground is . Riding with the wind his rate relative to the ground is .

If he goes 15 km in 1 hour, then his rate relative to the ground is 15 kph. If he goes 15 km in 36 minutes, remember that 6 minutes is .1 hour so 36 minutes must be .6 hour and his rate relative to the ground is

Now we can write:



or equivalently:



We can also write:



or equivalently:



But since , we can write:








The speed of the wind is 5 kph.

John