Question

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?

Answer 1

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

Answer 2

Answer: 3

Explanation:

It is useful to summarise the information in the form of a table with columns for distance, speed and time.

Remember if you know two of these, you can write an expression or answer for the third one.

s = d/t and t = d/s and d = s × t

We have that the speed on Monday was x miles per hour and the time, 1/2 an hour. We can find the distance as x × 1/2

Show this on the table and then complete it for Tuesday as well.

Distance Speed Time
−−−−−−−−−−−−−−−−−−−−−−−−
Monday 1/2 x x 1/2
Tuesday 1/2 x (x-2) 3/4

The speed on Tuesday can be given in two ways:

It is the same as on Monday (1/2 x) or as s × t

Form an equation: 3/4 (x-2) = 1/2 x

4 x 3/4 (x-2) = 4 x 1/2 x ← x 4

3 (x-2) = 2x

3x - 6 = 2x

x = 6 ← this was the speed on Monday.

The distance run on Monday was 1/2 x 6 = 3 miles