Question

Which speed is the fastest ? A)18 feet in 20 minutes B)90 feet in 2.5 hours C)20 yards in 1.5 hours D)3 2/3 yards in 15 minutes

Answer 1

D. 1 :1 ratio.

Explanation:

A is a ratio of .9:1 18/20 = 9/10 = .1
B. is a ratio of .4/1 `90/60 xx 2.5 = 90/150 = .6`
C. is a ratio of .66/1 = `(20 xx 3) /( 60 xx 1.5) = 60/90 = .66`
D. is a ratio of 1/1 `3 2/3 xx 3 / 15 = 15/15 = 1.0`

So D is the fastest.

Answer 2

`color(red)A)` is the fastest.

Explanation:

.

In order to compare, we need to convert all four speeds to a common unit. Let's convert them all to feet per hour:

`color(red)A)` `18` feet in `20` minutes

There are `60` minutes in each hour. We divide `18` by `20` to find the speed as feet per minute. Then we multiply the result by `60` to get feet per hour:

`18/20*60=9/10*60=9*6=` `color(red)("54 feet per hour")`

`color(red)B)` We divide `90` by `2.5` to get feet per hour:

`90/2.5=` `color(red)("36 feet per hour")`

`color(red)C)` There are `3` feet in each yard.

`20` yards is equal to `20*3=60` feet. We divide `60` by `1.5` to get feet per hour:

`60/1.5=` `color(red)("40 feet per hour")`

`color(red)D)` `3(2)/3=11/3`. We multiply `11/3` yards by `3` to get feet:

`11/3*3=11` feet

We divide `11` feet by `15` to get feet per minute and multiply the result by `60` to get feet per hour:

`11/15*60=` `color(red)("44 feet per hour")`

Therefore, `A` is the fastest.