Question

What is the ratio of 5 hours to 14 hours 10 minutes?

Answer 1

`6/17`

Explanation:

14 hours and 10 minutes is the same as `14 1/6` hours, which is the same as `(14xx6+1)6=85/6` hours.

This means the ratio is:
`5/(85/6)`

`=5xx6/85`

`=cancel(5)^1xx6/(cancel(85)^17)`

`=6/17`

Answer 2

`("5 hours")/("14 hours 10 minutes") =6/17`

Explanation:

To compare these values directly they need to be in the same units of measurement of time.

Notice that 10 minutes will divide exactly into 1 hour (60 minutes). So I choose the unit of measurement to be 10 minutes.

1 hour is 60 minutes which is 6 lots of 10 minutes.

So I hour is the a count of 6 units

`color(brown)("Count of 10 minutes in 14 hours 10 minutes")`
14 hours to count of 10 minutes `-> 14xx6 = 84`
Plus the 10 minutes from 14 hrs 10 min `" "color(white)(..)->ul(1)`
`" " 85`

`color(brown)("Count of 10 minutes in 5 hours")`
5 hours to count of 10 minutes `" "-> 5xx6 = 30`

`color(brown)("Determine the ratio")`

`("5 hours")/("14 hours 10 minutes") =30/85`

Divide top and bottom by 5

`(30-:5)/(85-:5) = 6/17`