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

dierdurst Aug 24, 2018

#1**+2 **

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

CPhill Aug 24, 2018