Question 766526
tricky little devil.
here's what i think.
manuel's rate of travel is x.
jose's rate of travel is 3 times that, so jose's rate of travel is 3x.
rate * time = distance
distance = 36
manuel's time is y + 2
jose's time is y


for manuel:
rate * time = distance becomes:
x * (y + 2) = 36


for jose:
rate * time = distance becomes:
3x * y = 36


you have 2 equations that need to be solved simultaneously.


simplify both equations to get:


xy + 2x = 36
3xy = 36


solve for xy in both equations.


you get:


xy = 36 - 2x
xy = 12


since both equations are equal to xy, you can set them equal to each other to get:


36 - 2x = 12


subtract 36 from both equations to get:


-2x = -24


divide both equations by -2 to get:


x = 12.


manuel rides his bike at 12 miles per hour.
jose drive his car at 36 miles per hour.


it takes manuel 3 hours to go 36 miles.
it takes jose 1 hour to go 36 miles.


it takes manuel 2 hours more than jose to go 36 miles.