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Home Q & A Board Science-Related Homework Help Mathematics
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irina irina
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11 years ago
A cyclist travels 60mi in 5 hours going against the wind. She travels 100 with the wind in the same amount of time. What is the rate of the cyclist in still air and what is the rate of the wind?
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wrote...
#1
11 years ago
60/5 = bike_speed - wind_speed
100/5 = bike_speed + wind_speed

solve for one variable in one equation and plug it in the second
wrote...
#2
11 years ago
Let x be the speed in still air
Let y be the speed of the wind
then (x - y) * 5 = 60 ==> x - y = 12
and (x + y) * 5 = 100 ==> x + y = 20
adding the two equations:
2x = 32 ==> x = 16

substituting in one:
16 - y = 12 ==> y = 4
Answer accepted by topic starter
RkamuRkamu
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#3
Posts: 171
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11 years ago
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#4
11 years ago
A proportion makes sense to me. 60/5=100/x so that's 500=60x then x would equal 8.3 hours. I think for rate you have to find the miles per hour, so that's 100/8.3 which is 12.05 miles per hour. I don't know how to find the wind though.
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