SOLUTION: Ruth bicycles 5km/h slower than bill. In the time that it takes Ruth to bicycle 42km, bill can bicycle 57km. How fast does each bicyclist travel?

Question 6024: Ruth bicycles 5km/h slower than bill. In the time that it takes Ruth to bicycle 42km, bill can bicycle 57km. How fast does each bicyclist travel?
Answer by Abbey(339) (Show Source): You can put this solution on YOUR website!
let bill's rate = x
let ruth's rate = x-5
bill's distance is 57 km
ruth's distance is 42 km
both times are the same, so use time=distance/rate and set the equations equal to one another
bill's equation:
time=57/x
ruth's equation:
time = 42/x-5

multiply by x(x-5) to clear the denominators:

add 285 to both sides:

subtract 42x from both sides:

divide both sides by 15:
so bill's rate is 19 kmh
and ruth's is 5 kmh slower, or 14kmh
check it to see:
57/19 = 3 hours
42/14= 3 hours

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