On Monday, you run treadmill for 1/2 hour at x miles per hour. On Tuesday, you walk the same distance on the treadmill, at 2 mph slower, and it takes you 3/4 hour. How many miles did you run on the treadmill on Monday?

Distance = rate * time

Let r = rate

Distance is the same for both runs,  so:

.5r = D =  3/4(r - 2)

Distribute (and convert .5):

2/4r = 3/4r - 3/2

Subtract 3/4 r from both sides:

-1/4r = -3/2

Multiply both sides by -4 to get a solitary r:

r = -3 * -4 / 2

r = 3 * 2

r = 6 miles per hour

.5 hours * 6 mi/hr = 3 miles

check:

6 - 2 = 4

3/4 hours * 4 mi/hr = 3 miles

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