- Twelve hungry teenagers can devour a very large pizza in 20 minutes. How many teenagers would it take to finish a very large pizza in 15 minutes? (Assume that all teenagers eat pizza at the same rate.)
- For a statue of Miss Levans, the amount of gold required is proportional to the square of the height of the statue. A statue of Miss Levans that is 20 feet tall requires 80 pounds of gold. How many pounds of gold does a statue that is 25 feet tall require?
- Tina lives 30 miles away from her work, and she normally drives at 45 miles per hour. If she wants to get to work 10 minutes earlier, how fast should she drive to work, in miles per hour?
- All of the members of our spray-painting team paint at the same speed. If 5 team members can paint a certain wall in 27 minutes, then how many minutes would it take 15 of our team members to paint the same wall?
- All of the members of our spray-painting team paint at the same speed. If 8 team members can paint a 5000 square foot wall in 30 minutes, then how many minutes would it take the 8 members to paint an 8000 square foot wall?
- All of the members of our spray-painting team paint at the same speed. If 12 team members can paint a 2400 square foot wall in 45 minutes, then how many minutes would it take for 9 team members to paint a 3600 square foot wall

Guest Nov 3, 2018

edited by
Guest
Nov 3, 2018

#1**+1 **

Mmmm.....that's a lot of stuff !!!....I'll do a few

Twelve hungry teenagers can devour a very large pizza in 20 minutes. How many teenagers would it take to finish a very large pizza in 15 minutes? (Assume that all teenagers eat pizza at the same rate.)

This is known as a "see-saw" problem

No. of teens * 15 = 12 * 20

No. of teens * 15 = 240 divide both sides by 15

No. of teens = 240 / 15 = 16

CPhill
Nov 3, 2018

#2**+1 **

For a statue of Miss Levans, the amount of gold required is proportional to the square of the height of the statue. A statue of Miss Levans that is 20 feet tall requires 80 pounds of gold. How many pounds of gold does a statue that is 25 feet tall require?

We need to find the proportinality constant, k

80 = k * 20^2

80 = k * 400 divide both sides by 400

1/5 = k

So

Lbs. required = k * 125^2 = (1/5)(25)^2 = 1/5 * 625 = 125 lbs

CPhill
Nov 3, 2018

#3**+1 **

Tina lives 30 miles away from her work, and she normally drives at 45 miles per hour. If she wants to get to work 10 minutes earlier, how fast should she drive to work, in miles per hour?

Distance / Rate = Time ...so.....

30 mi / 45 miles per hour = 2/3 hrs to get to work = 40 minutes

So...10 minutes less is 30 minutes...so

Distance / Time = Rate

30 mi / 30 min = 30 mi / (1/2) hr = 60 mi/ hr

CPhill
Nov 3, 2018

#4**+1 **

All of the members of our spray-painting team paint at the same speed. If 5 team members can paint a certain wall in 27 minutes, then how many minutes would it take 15 of our team members to paint the same wall?

We have three times the labor with 15 team members as with 5.....so...it should take 1/3 as long = 9 minutes

Mathematically

5 * 27 = x * 15 divide both sides by 15

5 * 27 / 15 = x

5 * 9 / 5 = x = 9 (mnutes)

CPhill
Nov 3, 2018

#5**+1 **

All of the members of our spray-painting team paint at the same speed. If 8 team members can paint a 5000 square foot wall in 30 minutes, then how many minutes would it take the 8 members to paint an 8000 square foot wall?

Each minute..... 5000/ 30 = 500/ 3 sq ft is being painted by the 8 people

So...the number of minutes it would take them to paint 8000sq ft =

8000 / [ 500/3] = 24000/ 500 = 48 min

Another way to see this is that 5/8 of the work is done in 30 min

So

30 / (5/8) = 30 * 8 / 5 = 240 / 5 = 48 min

CPhill
Nov 3, 2018

#6**+1 **

All of the members of our spray-painting team paint at the same speed. If 12 team members can paint a 2400 square foot wall in 45 minutes, then how many minutes would it take for 9 team members to paint a 3600 square foot wall

Each minute ...8 workers can paint 2400 / [ 45 ] = 160 / 3 sq ft /min

So....1 worker can paint 1/8 of this in one minute = 160 /3 * (1/8) = 20/3 sq ft / min

So....9 workers can paint 9 * (20 / 3) = 180 / 3 = 60 sq ft / min

So....to paint 3600 square ft will take the 9 workers 3600 / 60 = 60 min

CPhill
Nov 3, 2018