SOLUTION: Pablo can drive 5 times as fast as Oscar can ride his bicycle. If it takes Oscar 4 hours longer than Pablo to travel 90 miles, how fast can Oscar ride his bicycle?

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Question 279596: Pablo can drive 5 times as fast as Oscar can ride his bicycle. If it takes Oscar 4 hours longer than Pablo to travel 90 miles, how fast can Oscar ride his bicycle?
Found 5 solutions by mananth, ikleyn, josgarithmetic, greenestamps, MathTherapy:
Answer by mananth(16949) About Me  (Show Source):
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Pablo can drive 5 times as fast as Oscar can ride his bicycle. If it takes Oscar 4 hours longer than Pablo to travel 90 miles, how fast can Oscar ride his bicycle?
Let Oscar's speed be x
Pablo's speed = 5x
t= distance /rate
90/x = oscars tiem
PAblo's time = 90/5x
90/x + 4 = 90/5x
90/x-90/5x=4
450-90 /5x= 4
360 -90=20x
270 =20x
x= 13.5 mph


Answer by ikleyn(53742) About Me  (Show Source):
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.
Pablo can drive 5 times as fast as Oscar can ride his bicycle. If it takes Oscar 4 hours longer than Pablo
to travel 90 miles, how fast can Oscar ride his bicycle?
~~~~~~~~~~~~~~~~~~~~~~~~~~


        The solution and the answer in the post by @mananth both are incorrect due to arithmetic errors.
        I came to provide a correct solution. 


Let Oscar' speed be x miles per hour

Pablo's speed = 5x miles per hour

t= distance /rate

90%2Fx = Oscar's time

Pablo's time = 90%2F5x


Time equation

    90%2Fx + 4 = 90%2F5x


Simplify and find x

    90%2Fx - 90%2F5x = 4

    %2890%2Fx%29%2A%281-1%2F5%29 = 4

    %2890%2Fx%29%2A%284%2F5%29 = 4

    90%2Fx = 5

    x = 90%2F5 = 18.


ANSWER.  Oscar' speed riding bicycle is 18 miles per hour.

Solved correctly.



Answer by josgarithmetic(39790) About Me  (Show Source):
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              SPEED        TIME      DISTANCE

Pablo         5r           90/(5r)     90

Oscar          r           90/r        90

Difference                  4

highlight_green%2890%2Fr-90%2F%285r%29=4%29


45%2Fr-45%2F%285r%29=2
%285%2F5%29%2845%2Fr%29-45%2F%285r%29=2
%284%2A45%29%2F%285r%29=2
36%2Fr=2
18%2Fr=1
highlight%28r=18%29

Answer by greenestamps(13326) About Me  (Show Source):
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The ratio of the two speeds is 5:1.

Oscar takes 4 hours more than it takes Pablo to travel the 90 miles. If t is the number of hours Pablo takes to travel the 90 miles, then t+4 is the number of hours it takes Oscar to travel those 90 miles.

Since the distances are the same, the ratio of the two times is 5:1.

(t+4):t = 5:1

%28t%2B4%29%2Ft=5%2F1
5t=t%2B4
4t=4
t=1

It takes Oscar t+4 = 5 hours to travel the 90 miles, so his speed is 90/5 = 18 mph.

ANSWER: 18 mph

Answer by MathTherapy(10801) About Me  (Show Source):
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Pablo can drive 5 times as fast as Oscar can ride his bicycle. If it takes Oscar 4 hours longer than
Pablo to travel 90 miles, how fast can Oscar ride his bicycle?
**************************************************************
Let Oscar's riding-speed be S
Since Pablo's driving-speed is 5 times as fast as Oscar's riding-speed, then Pablo's driving-speed is 5S
With distance being 90 miles, Oscar's time to cover this distance = 90%2FS, while Pablo's is 90%2F%285S%29+=+18%2FS 
It's stated that "it takes Oscar 4 hours longer than Pablo to travel 90 miles....". This gives us the
following TIME equation: 90%2FS+-+18%2FS+=+4
                                          %2890+-+18%29%2FS+=+4 
                                                    72%2FS+=+4 
                                                    4S = 72 -- Cross-multiplying
            Oscar's riding-speed, or S+=+72%2F4+=+highlight%28matrix%281%2C2%2C+18%2C+mph%29%29