Question

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

Answer 1

Since the distance = speed*time we have:

(1/2)*x = (3/4)(x - 2)

........

........

x = 6 mi

You ran 6 miles on the treadmill on Monday.

Answer 2

recall your d = rt, distance = rate * time.

so, the distance "d" miles for each day is the same, however the rate on Monday is "x", whilst the rate on Tuesday is "x - 2".

$\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Monday&d&x&\frac{1}{2}\\\\ Tuesday&d&x-2&\frac{3}{4} \end{array} \\\\\\ \begin{cases} d=\frac{x}{2}\implies 2d=\boxed{x}\\\\ d=\frac{3}{4}(x-2)\\ ----------\\ d=\frac{3}{4}\left( \boxed{2d}-2 \right) \end{cases} \\\\\\ d=\cfrac{3(2d-2)}{4}\implies 4d=6d-6\implies 6=2d\implies \cfrac{6}{2}=d \\\\\\ 3=d$