SOLUTION: Jose can drive three times as fast as Manuel can ride his bicycle. If it takes Manuel 2 hours longer than Jose to travel 36 miles, how fast can Manuel ride his bicycle.

Question 766526: Jose can drive three times as fast as Manuel can ride his bicycle. If it takes Manuel 2 hours longer than Jose to travel 36 miles, how fast can Manuel ride his bicycle.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

Answer by MathTherapy(10556) (Show Source): You can put this solution on YOUR website!

Jose can drive three times as fast as Manuel can ride his bicycle. If it takes Manuel 2 hours longer than Jose to travel 36 miles, how fast can Manuel ride his bicycle.

Let Manuel�s speed = S
Then Jose�s speed = 3S

108 = 36 + 6S ----- Multiplying by LCD, 3S
6S = 108 � 36
6S = 72

S, or Manuel�s speed = , or mph

You can do the check!!

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