Question

Mitch can type 4 pages in 15 minutes. At this rate, how many pages can he type in 2 hours

Answer 1

This is a dimensional analysis problem. We see that mitch types at a rate of 4 pages per 15 minutes, so in fraction form it would look like this:

`\frac{4 \text{ pages}}{15 \text{ minutes}}`

So, what we want to do first is convert minutes to hours, so:

`\frac{4 \text{ pages}}{15 \text{ minutes}}*\frac{60 \text{ minutes}}{1 \text{ hours}}= \frac{16 \text{ pages}}{ 1 \text{ hour}}`

So, he types at a pace of 16 pages per hour, so that would mean he types 32 pages in 2 hours.

Answer 2

To solve this problem, we should set up a proportion, letting the variable x represent the unknown number of pages that Mitch can type in 2 hours.

4 pages/15 minutes = x pages/2 hours

However, because there are two different units in the denominators (minutes vs. hours), we must convert them to one unit before we can compare the values.

Because there are 60 minutes in 1 hour, to find the number of minutes in 2 hours, we must multiply 2 * 60.

2 * 60 = 120

Therefore, we can substitute 120 minutes into our proportion for 2 hours.

4 pages/15 minutes = x pages/120 minutes

We can now get rid of the units because they are the same on both sides of the equation.

4/15 = x/120

To simplify this proportion, we should use cross-multiplication. This means multiplying the numerator of one fraction by the denominator of the other and setting it equal to the product of the other numerator and the denominator.

(4)(120) = (15)(x)

We simplify by multiplying both sides of the equation out.

480 = 15x

Finally, we must divide both sides of the equation by 15 in order to get the variable x alone on the right side of the equation.

x = 32

Therefore, Mitch can type 32 pages in 2 hours.

Hope this helps!