SOLUTION: Martina leaves home at 9 A.M., bicycling at a rate of 24 mi/h. Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Martina leaves home at 9 A.M., bicycling at a rate of 24 mi/h. Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?      Log On


   

Question 70735: Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h. Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?
Found 2 solutions by checkley75, Nate:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
24T=48(T-2)
24T=48T-96
24T-48T=-96
-24T=-96
T=-96/-24
T=4 HOURS JOHN WILL CATCH UP WITH MARTINA
PROOF
24*4=48(4-2)
96=48*2
96=96

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h.
Martina has been cycling for two hours going 24 mi/h so she has already traveled 48 miles.
rate = 24
time = x
distance = 24x
already traveled 48 miles ~> 24x + 48 = distance
Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?
rate = 48
time = x
distance = 48x
When the distances are the same, they will meet.
48x = 24x + 48
24x = 48
x = 2 hours after John left
so ... 4 hours after 9:00 A.M.
1:00 P.M.