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?

Question 67532: 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?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
We'll determine how many hours it takes John to catch up and then add that to 11:00am-------------that will give us the answer
When the distances that both Martina and John have travelled are the same, then John will have caught up.
distance (d)=rate(r) times time(t)
d=rt
let t= time that has elapsed since John started
then (t+2) Martina's elapsed time

Martina's Distance=24mph(t+2)
Johns Distance=48t
When the distances that both Martina and John have travelled are the same, then John will have caught up.
24(t+2)=48t
24t+48=48t subtract 24t from both sides:
48=24t
t=2 hours-----------------'till they are both at the same place
11:00am+2 hours=1:00pm------------------------the answer we are looking for
CK
Martina's Distance=24mph(t+2)=24(4)=96 mi
Johns Distance=48t=48(2)=96 mi

Hope this helps----ptaylor

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