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Question

A boy starts to walk to school, which is 20 miles away at 6:50 and at 3 MPH. Then his dad picks him up and drives the rest of the way at 30 MPH. If he arrived at school at 9:00, how far did he walk?

Answer 1

You know he traveled on foot or car for 130 minutes (6:50 - 9:00).

 

Let x be the number of minutes he traveled on foot. 

Also note that 3mph = 1/20 miles per minute. 

Similarly, 30mph = 1/2 mile per minute.  You get this by diving each by 60 and you want to do this so you have minutes throughout.

 

x(1/20) + (130-x)(1/2) = 20

 

x/20 + (130-x)/2 = 20

 

x/20 + 10(130 - x)/20 = 20

 

(x + 1300 - 10x)/20 = 20

 

(1300 - 9x)/20 = 20

 

1300 - 9x = 400

 

- 9x = -900

x = 100

 

That means he walked for 100 minutes at 1/20 miles per minute or for 5 miles, at which point his dad picked him up at 8:30.