Question 6024
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/x=42/(x-5)}}}
multiply by x(x-5) to clear the denominators:
{{{57x-285=42x}}}
add 285 to both sides:
{{{57x=42x+285}}}
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