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Samantha begins biking at 12 mph from the center of town towards the ocean at 12:00 noon. Later that day, at 1:15 pm, Anthony begins biking along the same route as Samantha at 15 mph. How many miles will Samantha have covered when Anthony catches her?

 Apr 8, 2019
 #1
avatar+99580 
+2

Note that the distance that Samantha covers BEFORE Anthony starts =

 

Rate * Time  =

 

12 * (1 + 1/4)hrs =

 

12 * (1.25)  =  15 miles

 

And each hour....the distance that he closes on Samantha =  15 - 12  =  3 miles

 

So....the time it will take to catch her is

 

Distance Samantha is ahead                       15

___________________________  =        ______   =     5 hrs

 Distance Anthony closes per hour               3

 

 

cool  cool cool

 Apr 8, 2019
 #2
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+1

But its asking for the number of miles she traveled before she wwas caught up to

 Apr 8, 2019
 #4
avatar+99580 
+1

Sorry...we just need to take his rate * 5 hrs  =  15 * 5  = 75 miles...!!!!

 

 

cool cool cool

CPhill  Apr 8, 2019
 #3
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+1

Another way:

 

12T = 15(T-1.25), solve for T
T = 6.25 - hours will have passed from noon.
6.25 x 12 mph = 75 miles - when Anthony catches up with her.

 Apr 8, 2019

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