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?

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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) About Me  (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
57%2Fx=42%2F%28x-5%29
multiply by x(x-5) to clear the denominators:
57x-285=42x
add 285 to both sides:
57x=42x%2B285
subtract 42x from both sides:
15x=285
divide both sides by 15:
x=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