College Algebra

Question

Oscar can drive 4 times as fast as Pablo can ride his bicycle. If it takes Pablo 3 hours longer than Oscar to travel 84miles, how fast can Pablo ride his bicycle?

Answer 1

Oscar:  84 = 4rt

Pablo : 84 = r*(t+3)

 

4rt = r ( t+3)

 

4rt = rt + 3r

 

3rt = 3r

 

t = 1

 

Oscar:

81 = 4rt = 4r(1) = 4r

r = 21

 

Pablo:

    81 = 21*(3+1)

 

Pablo can ride the bicycle 21 miles per hour.

It will take him 4 hours to travel the 84 miles.

 

Oscar drive 21x 4 = 84 miles per hour.

He travels the 84 miles in 1 hour, or 3 hours faster.

 

 

 

 

Answer 2

Hi Johnny.

 

Let's assign some variables.  "O" looks too much like "0" so we will NOT use "O" for Oscar...

 

Let "k" be the speed Oscar drives

Let "p" be the speed Pablo rides his bike.

 

Remember that dist = rate*time, or time = dist / rate

 

k=4p   (Oscar drive 4 times as fast as Pablo)

 

time for Pablo is 84/p

time for Oscar is 84/k

 

since it takes Pablo 3 hours longer, 84/p = 84/k + 3

Look at this as "time for Pablo (84/p) is (=) 3 hours longer than Oscar (84/k +3)"

 

Now you have two equations and two unknowns.  We know that k=4p from above.  

Substitute k=4p in for every "k" in 84/p = 84/k + 3

 

84/p = 84/(4p) + 3    (reduce the 84/4 = 21)

 

84/p = 21/p + 3        (put all of the "over p"'s on the left side)

                                subtract 21/p from both sides

63/p = 3                   Now solve for p, by mult both sides by p

 

63 = 3p                 Now divide both sides by 3

 

21 = p      Looks like Pablo can ride his bicycle 21 miles per hour.

 

 

Now lets check:

How long will it take Pablo to go 84 miles?   4 hours  (84/21)

How long will it take Oscar to go 84 miles?  Well, if p = 21, k=4p, then Oscar drives 84 miles per hour.  So it takes Oscar 1 hour to go 84 miles.  And Pablo's 4 hours is 3 hours longer than Oscars 1 hour.  Looks like we got the right answer.  Yay us!