SOLUTION: A long-distance runner starts on a course running at an average speed of 6mph. Half an hour later, a second runner begins the same course at an average speed of 7mph. How long afte

Algebra ->  Expressions-with-variables -> SOLUTION: A long-distance runner starts on a course running at an average speed of 6mph. Half an hour later, a second runner begins the same course at an average speed of 7mph. How long afte      Log On


   

Question 1154837: A long-distance runner starts on a course running at an average speed of 6mph. Half an hour later, a second runner begins the same course at an average speed of 7mph. How long after the second runner starts will the second runner overtake the first runner?
Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The second runner starts a half hour after the first. Since the first runner runs at 6mph, he has run 3 miles when the second runner starts.

The second runner runs 1mph faster than the first. The amount of time he needs to make up the 3 miles, at the rate of 1mph, is 3 hours.

ANSWER: 3 hours

Algebraically....:

x = hours the second runner runs
x+0.5 = hours the first runner runs

7x = distance second runner runs
6(x+0.5) = distance first runner runs.

7x+=+6%28x%2B0.5%29
7x+=+6x%2B3
x+=+3

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

Since both are running in same direction catchup speed is 7-6 = 1 mph
I runner is 3 miles ahead when II runner starts
Catch up distance = 3 mi
catch uptime = 3/1 = 3 hours