Rational Equations

Question

After cycling at a steady rate for 60 miles, Cecil had a flat tire. He walked 8 miles to a repair shop. Cecil's cycling rate was 3 times faster than this walking rate. If the time spent cycling and walking was 7 hours, at what rate was 'Cecil riding his bike?

Answer 1

First set up the variables:  Suppose his walking rate was x miles per hour.  Then his cycling rate would be 3x.

 

Now, he biked for 60 miles, so the time he spent biking was 60 / 3x = 20 / x.  (That's because speed * time = distance, so distance / speed = time.)

 

And his walking time was 8 / x.

 

So the total time he spent was 20/x + 8/x and that was 7 hours.  That gives us an equation:

 

20/x + 8/x = 7

 

Let's solve it.  First simplify the left side:

20/x + 8/x - 7

28/x = 7

 

Multiply both sides by x to get x out of the denominator:

28 = 7x

 

Divide both sides by 7:

4 = x

 

So his walking rate was 4 mph, and his biking rate was 3 times that, or 12 mph.