SOLUTION: A cyclist travels 54 miles in 6 hours going against the wind and 52 miles in 4 hours with the wind. What is the rate of the cyclist in still air and what is the rate of the wind?

Question 317833: A cyclist travels 54 miles in 6 hours going against the wind and 52 miles in 4 hours with the wind. What is the rate of the cyclist in still air and what is the rate of the wind?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let speed of cycle be x in still air
speed of wind =y
..
6(x-y)=54
4(x+y)52
..
6x-6y=54
x-y=9
4x+4y=52
x+y=13
..
add the two equations
x-y+x+y=22
2x=22
x=11 mph. speed of cycle
x-y=9
11-y=9
y=2
speed of wind = 2 mph

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