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A man starts out on a trip driving his car at a constant rate of 48 mph. A man riding a motorcycle starts out on the same route 12 hours later, traveling at a constant rate of 64 mph. How long will the car have been traveling when the motorcycle catches up?

 Jan 12, 2020
 #1
avatar+18295 
+1

Let  t  be the number of hours that the person drives his car.  Therefore, his total distance is  48·t.

The man on the motorcycle starts out 12 hours later. Therefore, his amount of time is  t - 12  and his total distance is  64·(t - 12).

Since these two distances are equal:  48t  =  64(t - 12)

Solving:                                                48t  =  64t - 768

Subtracting  64t  from both sides:       -16t  =  -768

Dividing both sides by  -16:                     t  =  48 hours   (for the car)

 Jan 12, 2020
 #2
avatar+20254 
+2

At 12 hours the car has gone 48 x 12 =    576 miles

   the motorcycle is traveling   64-48 = 16 mph faster

      to cover 576 miles , the motorcycle will take   36 hours at which time the car will have been travelling 12 + 36 = 48 hours

 Jan 12, 2020

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