Middle School

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It takes 5 minutes to fill a twin-size air mattress (39 by 8.75 by 75 inches). How long will it take to fill a queen-size mattress (60 by 8.75 by 80 inches)?

Answer :

The total volume of the twin size air mattress is 25593.75

It takes 5 minutes per 25593.75 cubed inches.

That is 5 over 25593.75, written like: 5/25593.75

The total volume of the queen sizes mattress is 42000.

It takes ? minutes per 42000 cubed inches.

That is ? over 42000, written like: ?/42000

Those are both proportions. We know those proportions will be equal. So, our problem is:

5/25593.75 = ?/42000

So solve this, we have to cross multiply and then solve the equation. We will substitute x for the question mark. The equation, after cross multiplying is:

25,593.75x = 210,000

Divide both sides by 25,593.75 to eliminate it.

x = 8.2

It takes 8.2 minutes to fill the queen sized air mattress. (If instructed to round to the nearest whole number, the answer would be 8.)

Let me know if you have any other questions about this! :)

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Rewritten by : Barada

We want to find the rate at which the volume is filled and use that to find how long takes to fill a queen-sized mattress.

We will define the rate as the quotient between the volume filled and the time it takes to fill that volume.

We will see that the answer is 8.2 minutes.

The given information is that it takes 5 minutes to fill a mattress of 39 by 8.75 by 75 inches

Remember that for a rectangular prism of length L, width W, and height H has a volume:

V = L*W*H

Then the volume of the mattress is:

V = (39 in)*(8.75 in)*(75 in) = 25,593.75 in^3

Then the rate is:

r = (25,593.75 in^3)/(5*60 s)

Where i wrote the time in seconds instead of minutes:

r = (25,593.75 in^3)/(300 s) = 85.3125 in^3/s

Now we want to know how long takes to fill a queen-sized mattress, the volume of this mattress is given by:

V = (60 in)*(8.75 in)*(80 in) = 42,000 in^3

Let's assume that it takes a time T, then we can write:

( 85.3125 in^3/s)*T = 42,000 in^3

Now we can solve this for T:

T = (42,000 in^3)/(85.3125 in^3/s) = 492.3 seconds.

Now we can divide this by 60 to transform the time to minutes:

492.3 s = (492.3/60) min = 8.2 minutes.

If you want to learn more, you can read:

https://brainly.com/question/12797552