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

`3` miles run on Monday

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 = sxxt`

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 xx 1/2`

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

`color(white)(wwwwww)ul("Distance Speed Time")`

Monday`|" "1/2xcolor(white)(wwwww)xcolor(white)(wwwww) 1/2`

Tuesday`|" "1/2xcolor(white)(wwww)(x-2)color(white)(www) 3/4`

The speed on Tuesday can be given in two ways:

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

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

`4xx3/4(x-2) =4xx 1/2x" "larrxx 4`

`3(x-2) = 2x`

`3x-6 = 2x`

`x = 6" "larr` this was the speed on Monday.

The distance run on Monday was `1/2 xx6 = 3` miles