SOLUTION: If Martina leaves home at 9 A.M., bicycling at a rate of 24 mi/h. About two hours later, John leaves, driving at the rate of 48 mi/h. What will the time be when John catches up wi

Algebra ->  Inequalities -> SOLUTION: If Martina leaves home at 9 A.M., bicycling at a rate of 24 mi/h. About two hours later, John leaves, driving at the rate of 48 mi/h. What will the time be when John catches up wi      Log On


   

Question 54013: If Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h. About two hours later, John leaves, driving at the rate of 48 mi/h. What will the time be when John catches up with Martina?
Found 2 solutions by checkley71, AnlytcPhil:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
24X=48(X-2) OR 24X=48X-96 OR 24X=96 OR X=4 HOURS JOHN WILL CATCH MARTINA
PROOF 24*4=48(4-2) OR 96=48*2 OR 96=96

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
If Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h. About two hours later, John leaves, driving at 
the rate of 48 mi/h. What will the time be when John 
catches up with Martina?

Make a DRT-chart:

          Distance    Rate    Time
Martina                           
John                                 

Fill in their rates (speeds) 

          Distance    Rate    Time
Martina                24         
John                   48         

Let x be the time after 9 o'clock that John catches up
with Martina.  So Martina's time is x hours, so fill
that in:

          Distance    Rate    Time
Martina                24       x
John                   48         

Since John started two hours later, his time was 2 hours
less than Martina's time.  So his time is x-2 hours. Fill
that in 

          Distance    Rate    Time
Martina                24       x
John                   48      x-2

Now use the fact that Distance = Rate × Time to fill in
the two distances:

          Distance    Rate    Time
Martina      24x       24       x
John       48(x-2)     48      x-2

They traveled the same distance, so we can set their
distances equal to each other:

  24x = 48(x-2)

Solve that and get x = 4 hours.

Four hours after 9 AM is 1 PM.

Edwin