Question

Doogle drove 30 and one-third miles toward his brother's house in one-third of an hour. About how long will the entire 100-mile trip take at this constant speed?

Answer 1

`1(9)/(91)\ hours`

Explanation:

we know that

30 and one-third miles is equal to

`30(1)/(3)\ mi=(30*3+1)/(3)=(91)/(3)\ mi`

one-third of an hour is equal to

`(1)/(3)\ h`

Applying proportion

`((1/3))/((91/3))(h)/(mi)=(x)/(100)(h)/(mi)\\ \\x=(100)/(91)\ h`

Convert to mixed number

`(100)/(91)\ h=(91)/(91)+(9)/(91)=1(9)/(91)\ h`

Answer 2

The entire 100-mile trip will take 1 hour and 6 minutes to complete.

Explanation:

Doogle drove 30 1/3 miles or 30.33 miles toward his brother's house in one-third of an hour.

1/3 of an hour =
`(1)/(3)*60=20` minutes.

Lets say the speed is constant.

So, 30.33 miles are covered in 20 minutes.

Then 100 miles will be covered in =
`(20)/(30.33)*100`

= 65.94 minutes or 1.099 hours.

That becomes almost 1 hour and 6 minutes. (
`0.099*60=5.94` ≈6)

Therefore, the entire 100-mile trip will take 1 hour and 6 minutes to complete.