SOLUTION: I have been struggling on this math problem for a while now and I was wondering if anyone could help me? I would deeply appreciate it! Please and Thank You! Rate-Time-Distance

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Question 134561This question is from textbook Algebra Structure and Method
: I have been struggling on this math problem for a while now and I was wondering if anyone could help me? I would deeply appreciate it! Please and Thank You!
Rate-Time-Distance Problems
Solve.
At 7:00am Joe starts jogging at 6mi/h. At 7:10am Ken starts off after him. How fast must Ken run in order to overtake him at 7:30am? This question is from textbook Algebra Structure and Method

Answer by solver91311(24713) About Me  (Show Source):
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Ken's running speed: x
Joe's running speed: 6 mph

Since we want to know about how fast Ken is running when he catches Joe, the distance they travel must be the same.

We also know that Joe is running for 30 minutes or one-half hour, and Ken is running for 20 minutes or one-third of an hour.


Joe's trip:
d=6%2A%281%2F2%29=3 miles

Ken's trip:
d=x%2A%281%2F3%29 and that must also equal 3 miles.

x%2A1%2F3=3

x=9 miles per hour.

Check:
Joe: 6 mph for 1/2 hour = 3 miles
Ken: 9 mph for 1/3 hour = 3 miles