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Charlie biked 15 minutes home from school and then walked 12 minutes to the pizza place near his house. This trip was 3.6 miles in total. His rate on his bike is 3 miles per hour less than 5 times his walking rate. In miles per hour, what is Charlie’s speed as he walks and what is his speed as he bikes?

 Apr 10, 2020
 #1
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Let  the  rate  he walks  = W

Then the rate he bikes  = 5W  - 3

Note that we need to convert  minutes  to hours :

15 min = 1/4 hr

12 min   =1/5  hr

 

And   note  that

 

rate on bike * time  +  walking rate * time  =total distance

 

So

 

(5W - 3) (1/4)  +  (W)(1/5)  = 3.6       simplify

 

(5/4)W - 3/4  + (1/5)W  =  3.6                { 5/4  = 1.25 , 3/4 = .75, 1/5  = .2  }

 

1.25W  - .75 + .2W  = 3.6

 

1.45W - .75  = 3.6      add .75 to both sides

 

1.45W  = 4.35      divide both sides by 1.45

 

W  = 3  mph  = walking rate

 

Biking rate  = 5(3)  - 3   =  12 mph

 

 

cool cool cool

 Apr 10, 2020

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