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A person rides a bike against the wind at 8 mph when he goes back the wind helps him. He traveled 4 miles total 2 to the shop and 2 back. If the round trip was 30 minutes longwhat is thomas's speed on the bike without the wind.

 Jul 18, 2022
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Distance / Rate  =  Time

 

30 mi = 1/2 hr

 

2 / ( r - 8)  +  2  / ( r + 8)  =   1/2             where r is his rate in  still air

 

Multiply through by  2

 

4 / (r - 8)   + 4/(r + 8)  = 1

 

[4 ( r + 8) + 4(r - 8)] / [ (r -8) (r + 8)  = 1

 

8r   =  (r - 8) (r + 8)

 

8r  = r^2   -  64

 

r^2 - 8r  - 64  = 0

 

r^2  - 8r  =   64

 

r^2  -8r + 16  = 64 + 16

 

(r - 4)^2  =  80         take the positive  root

 

r -4 =   sqrt (80)

 

r =  sqrt (80) + 4  ≈    12.9 mph =   his rate in  still air 

 

 

cool cool cool

 Jul 18, 2022

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