Question

You have from 10 p.m. to 11:30 p.m. to do a project. a. At 11, what fraction of the time remains? b. At 11:20, what fraction of the time remains?

Answer 1

a.
`(1)/(3)`

b.
`(1)/(9)`

Explanation:

To solve it we must work in a single unit of time.

The unit we will use to solve it will be in minutes

So from 10 pm to 11 pm, it has been 1 hour (60 minutes) and from 11 pm to 11:30 pm has been half an hour (30 minutes)

Now the total minutes that have passed from 10 pm to 11:30 pm is

`60+30= 90`

A fraction tells us how many parts we have

In this case 90 minutes is what we want to divide:

a. At 11, what fraction of the time remains?

Let's think about it in the following way if 60 minutes have passed from 10 pm to 11 pm, at what fraction of 90 minutes does 60 minutes equal?

To solve it we use a simple rule of three

`90 \longrightarrow 1\\ 60\longrightarrow x \\ \\ x=((60)(1))/(90) \\ x=(2)/(3)`

This is the fraction of time that has past.

Now the fraction of time that remains is

`1-(2)/(3)=(1)/(3)`

b. At 11:20, what fraction of the time remains?

Let's think about it in the following way if 80 minutes have passed from 10 pm to 11:20 pm, at what fraction of 90 minutes does 80 minutes equal?

To solve it we use a simple rule of three

`90 \longrightarrow 1\\ 80\longrightarrow x \\ \\ x=((80)(1))/(90) \\ x=(8)/(9)`

This is the fraction of time that has past.

Now the fraction of time that remains is

`1-(8)/(9)=(1)/(9)`