SOLUTION: Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster than his running speed. What is his running speed?

Based on the given data, I can guess the answer in 5 seconds.


    His running speed is 5 miles per hour.


CHECK.  He spent 1 hour running and  = 4 hours biking.

Let x be the running speed, which is the value under the question.

Then his biking speed is  (x+15) miles per hour.


The time spent running is    hours.

The time spent biking is  .


The total time is 5 hours; it gives you and equation


     +  = 5   hours.


It is so called "time" equation.

As soon as you got it, the setup is just completed.

Now your task is to solve it.


For it, multiply both sides by x*(x+15).  You will get


    5*(x+15) + 80x = 5x*(x+15)

    (x+15)   + 16x = x*(x+15)

    17x + 15       = x^2 + 15x

     x^2 - 2x - 15 = 0

     (x-5)*(x+3)    = 0


Of the two roots, x= 5  and  x= -3, only positive x= 5 makes sense.


So, your answer is:  the running speed is  5 mph;  same as I guessed at the beginning.