SOLUTION: A jogger starts from one end of a 12-mile nature trail at 8:00 A.M. One hour later, a cyclist starts from the other end of the trail and rides toward the jogger. If the rate of the

Algebra ->  Equations -> SOLUTION: A jogger starts from one end of a 12-mile nature trail at 8:00 A.M. One hour later, a cyclist starts from the other end of the trail and rides toward the jogger. If the rate of the      Log On


   

Question 1024859: A jogger starts from one end of a 12-mile nature trail at 8:00 A.M. One hour later, a cyclist starts from the other end of the trail and rides toward the jogger. If the rate of the jogger is 6 mph and the rate of the cyclist is 12 mph, at what time will the two meet?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                   rate             time          distance

JOGGER              6               t+1

CYCLIST            12                t

BOTH TOTAL                                         12


The two meet when the sum of their distances traveled becomes 12 miles. 


                   rate             time          distance

JOGGER              6               t+1          6(t+1)

CYCLIST            12                t           12t

BOTH TOTAL                                         12


highlight%286%28t%2B1%29%2B12t=12%29
Solve for t, quantity in hours.
This t is the number of hours past 8:00AM when the jogger and the cyclist meet.



SOLUTION STEPS FOR THE EQUATION
6t%2B6%2B12t=12
18t%2B6=12
18t=6
t=6%2F18
highlight%28t=1%2F3%29, which is 20 minutes.

They meet at 9:20AM.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A jogger starts from one end of a 12-mile nature trail at 8:00 A.M. One hour later, a cyclist starts from the other end of the trail and rides toward the jogger. If the rate of the jogger is 6 mph and the rate of the cyclist is 12 mph, at what time will the two meet? 
They meet 1%261%2F3 hours after the jogger begins or 1%2F3 hour after the cyclist begins, which is: highlight_green%28matrix%281%2C2%2C+9%3A20%2C+AM%29%29