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  1. 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.)
  2. 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?
  3. 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?
  4. 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?
  5. 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?
  6. 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
  7.  
Guest Nov 3, 2018
edited by Guest  Nov 3, 2018
 #1
avatar+91360 
+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

 

 

cool cool cool

CPhill  Nov 3, 2018
 #2
avatar+91360 
+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

 

 

cool cool cool

CPhill  Nov 3, 2018
 #3
avatar+91360 
+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   

 

 

cool cool cool 

CPhill  Nov 3, 2018
 #4
avatar+91360 
+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)

 

 

cool cool cool

CPhill  Nov 3, 2018
 #5
avatar+91360 
+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

 

cool cool cool

CPhill  Nov 3, 2018
 #6
avatar+91360 
+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 

 

 

cool cool cool

CPhill  Nov 3, 2018

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