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on a 75 mile trip, Mr.Jones average rate for the first 15 miles was 10 miles per hour less than his average rate for the remainder of the trip. His time for the entire trip was two hours. Find his average rate for the first 15 miles.

 Mar 19, 2021
 #1
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Distance  / rate  =  total time

 

So

 

time for first 15 miles +  time for last 60 miles =   2 hrs  ....so.....

 

15 /  r    +  (75 - 15)  / ( r + 10)  =  2         simplify

 

15 / r  +  60 / (r + 10)  =  2

 

15 ( r + 10)  + 60r

_______________   =  2

         r ( r + 10)

 

15r + 150 + 60r   =  2  r  ( r + 10)

 

75r  + 150  =  2 ( r^2 + 10r)

 

75r  + 150  =  2r^2  +  20r       rearrange  as

 

2r^2 - 55r - 150  = 0        factor  as

 

(2r + 5) ( r - 30)  = 0

 

The  second factor set to 0   gives us what we need

 

r   - 30   = 0

 

r = 30  (mph) =   the  rate during the  first 15 miles

 

 

cool cool cool

 Mar 19, 2021

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