SOLUTION: Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 mi/h faster than Charlene. They meet in 5 hours. Find Charlene's speed.

Question 108109: Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 mi/h faster than Charlene. They meet in 5 hours. Find Charlene's speed.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let C be Charlene's rate
.
Since Paul's rate is 16 mph more than C, then we can write that Paul's rate is C + 16.
.
The distance each travels is their rate times the time that they drive at their rate. That
means that Charlene travels C*T miles. But T is given as 5 hours. Therefore, the distance that
Charlene travels in the 5 hours is 5*C. Meanwhile, Paul's rate times the time that he travels
at that rate is (C + 16)*T, and since T = 5 hours, the distance that Paul travels is 5*(C + 16).
This multiplies out to a distance of 5C + 80.
.
The problem says that the total distance that is to be covered by the two drivers is
420 miles. In equation form, the sum of the distances covered by the two drivers is:
.
5C + 5C + 80 = 420
.
Add the two terms on the left side that contain C to get:
.
10C + 80 = 420
.
Get rid of the 80 on the left side by subtracting 80 from both sides to get:
.
10C = 420 - 80 = 340
.
Solve for C (Charlene's rate) by dividing both sides by 10 to get
.
C = 340/10 = 34 mph
.
You were asked to find Charlene's speed, and you have it .... 34 mph. [Paul's rate is 16
mph faster, so Paul drives at 50 mph.]
.
Hope this helps you to understand the problem and to see how to find the solution.
.

RELATED QUESTIONS
Paul and Charlene are 420 miles apart. They start toward each other with Paul driving... (answered by josmiceli,ankor@dixie-net.com,checkley71)

paul and frank are on the same path 39.15 miles apart. they are going to ride their bike... (answered by mananth)

Two cars start from towns 420 miles apart and travel toward each other. They meet at 4... (answered by ikleyn)

Corey is 138 miles away from Paul. They are traveling towards each other. If Paul travels (answered by ikleyn)

Two cars start at the same time from the same point and travel in opposite directions.... (answered by Mathtut)

Two cars start at the same time from the same point and travel in opposite directions.... (answered by Alan3354)

estion Two cyclists leave towns 96 miles apart at the same time and travel... (answered by josgarithmetic)

Two buses leave towns 432 miles apart at the same time and travel toward each other. One... (answered by ankor@dixie-net.com)

Two cyclists, 120 miles apart, start riding toward each other at the same time. One... (answered by rfer)