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Adam started to run at a rate of 6 mph from city A towards city B, which is 18 miles away. Ten minutes later, Benjamin started to run from city B towards city Aand simultaneously, Caroline started to bicycle at a rate of 11 mph from city A towards city B. If Caroline caught up to Benjamin 50 minutes after passing Adam, what was Benjamin's rate in mph?

 Mar 30, 2020
 #1
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 Mar 30, 2020
 #2
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Adam runs  at 6mph  =  (6/60)*88  = 8.8 ft / s

 

Caroline  bikes  at  (11/60)* 88  =  242/15 ft/s

 

When Caroline  starts to ride, Adam  will have biked  (8.8)ft/s  * 600s  =  5280 ft

 

So....it will take  Caroline  (5280) / (242/15  -  8.8)   =  720  sec   to catch  Adam  = 12 min

 

50 + 12  =  62  min  after  this  she  passes  Benjamin =  time  that Benjamin has ridden

 

So   she has  biked  62 * 60 ( 242/15)  =  60016 ft  =  341/30  mi

 

So....Benjamin has run 18  - 341/30  = 199/30  mi in 62  min

 

So.....his  rate  is     (199/30)mi  ( 60/62)  ≈  6.42 mi/hr

 

 

cool cool cool

 Mar 30, 2020

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