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# Rate Problem

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Sam leaves home at the same time each morning and drives directly to work. If his travel speed averages \(30\) mi/h, he will be \(18\) minutes late for work. If his travel averages \(45\) mi/h, he will arrive \(8\) minutes early. What is the total number of miles between Sam's home and work?

- Daisy

Aug 24, 2018
edited by dierdurst  Aug 24, 2018
edited by dierdurst  Aug 24, 2018
edited by dierdurst  Aug 24, 2018

### 1+0 Answers

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Let  x  be the number of minutes it would normally take to drive the route

Since

R * T  = D     and  D  is the same in both cases, we have that

30 ( x + 18)  = 45 (x  - 8)        simplify

30 x + 540  = 45 x - 360     rearrange as

540 + 360 = 45x - 30x

900 = 15x  divide both sides by 15

60  = x

So....the distance  is  30 (60 + 18)  = 30 mph ( 78  min)

But  we need to  convert 78 min to hours =  78/60  = 39/30 hr

So...the total distance is  30m/h ( 39/30 h)  = 39 miles

Aug 24, 2018
edited by CPhill  Aug 24, 2018