Question

David and Brad are competing in a 20-mile bicycle race. David rides 6.2 miles in 1/4 hour. Brad rides 11.9 miles in 1/2 hour. If both riders continue at the same average speed, who will finish first? Explain how you know.

Answer 1

First, you calculate David's and Brad's unit rate. 

David:

6.2 mi./1/4 hr. = 6.2 m./15 minutes 
In an hour, there's 60 minutes. 60 divided by 4 is 15. So 1/4 of an hour is 15 minutes.

Brad:

11.9 mi./1/2 hr. = 11.9 mi./30 minutes
Once again, there's 60 minutes in an hour, so 1/2 of an hour is 30 minutes.

Okay, observing both of the unit rates, David's speed is just about half of Brad's speed. As a result, you multiply David's unit rate twice to get the same amount of time as Brad. It's easier to solve if you think about fractions since unit rates and fractions are just about the same. Now, multiply both the numerator and denominator by 2:

6.2 x 2 = 12.4, and 15 x 2 = 30
Now that you've multiplied them by two, David and Brad are now continuing at the same average speed.

David: 12.4 mi./30 min.
Brad: 11.9 mi./30 min.

David will finish the bicycle race first since he's gone farther than Brad.
I really hope I helped! :) There are so many other ways to solve this, but here's one way that I know best. If I didn't help, I'm sorry. I tried. :(