college algebra(rational equation application)

Question

Carl and Mike start a 3 mile race at the same time. If Mike ran the race at 6 miles per hour
and finishes the race 10 minutes before Carl, how fast does Carl run?

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use on this one is

Time = Distance / Speed

Mike’s time here was 3 miles / 6 mph = 0.5 hours

Meaning that Carl’s time was (0.5 hours x 60 minutes/hour) + 10 minutes = 40 minutes in order to run the 3 miles race

To find Carl’s speed then we can take

3 miles / (40 minutes x 1 hour/60 minutes) = 4.5 mph

So Carl ran the race at a speed of 4.5 miles per hour

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

d = rt, so t = d/r and r = d/t

 

t = 3/6 = 1/2 = 30 minutes

 

40 minutes = 40/60 = 2/3 hours

 

r = 3/(2/3) = 9/2

 

Carl runs 4.5 mph.