Phillip R. answered • 09/01/14

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Emily C.

asked • 09/01/14So I have no idea what to do

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Phillip R. answered • 09/01/14

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Top Notch Math and Science Tutoring from Brown Univ Grad

56 minutes for 5 people to paint 10 walls

multiply by 5 to get 1 person

divide by 7 to get 7 people

divide by 10 to get 1 wall

multiply by 8 to get 8 walls

(56)5*8)/(10*7) minutes for 7 people to paint 8 walls

2240/70 = 32 minutes

John M. answered • 09/01/14

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Emily,

First we need to calculate the painting "rate." A rate is something like miles per hour, that is to say an amount of something (i.e. miles) done in a unit of time (i.e. minutes). In this case our generic rate is painted-walls per minute per person. So, our base rate is 10 walls per 56 minutes per 5 people. Now treat every "per" as a division, so we can transform our rate into 10/56 of a wall, per minute per 5 people and then divide by 5 persons which means our rate is 2/56 (which reduces to 1/28) of a wall per minute per person.

Now we need to create an equation using this rate to calculate the number of minutes for 7 people to paint 8 walls. I find the best way is to keep track of the units. Generally, a rate x # of people x time = work, so our generic equation is

2 walls 7 persons # minutes 8 walls

-------------------- x -------------- x ---------------- = -----------

56 person - minute 1 1 1

2 walls x 7 persons # minutes 8 walls

-------------------- x -------------- = -----------

56 person - minute 1 1

-------------------- x -------------- = -----------

56 person - minute 1 1

14 walls # minutes [ 56 minute ] 8 walls [ 56 minute ]

------------ x -------------- x [ --------------- ] = ----------- x [ -------------- ]

56 minute 1 [ 14 walls ] 1 [ 14 walls ]

------------ x -------------- x [ --------------- ] = ----------- x [ -------------- ]

56 minute 1 [ 14 walls ] 1 [ 14 walls ]

= 8 x 56 / 14 = 32 minutes

Finally, a reality check. It took 5 people 56 minutes to paint 10 walls, now we have more people (7) and fewer walls (8) to paint, so they should be able to do it faster and 32 minutes is less than 56 minutes, so our answer makes sense.

I hope this helps.

it takes 56 minutes for 5 people to paint 10 walls

it takes 56 minutes for 1 person to paint 2 walls

it takes 56 minutes for 4 people to paint 8 walls

if we had 8 people we could paint the 8 walls in half the time (4/8), or 28 minutes

we have only 7 people so it will take not 4/8 of the time but 4/7 of the time

(4/7)*56=32 minutes

John G. answered • 09/01/14

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We have 56 minutes is the time taken for 5 people to paint 10 walls, which means that one person can paint 2 walls in 56 minutes. The reason for that is, given that each of the 5 people are working on their own walls and/or don't hinder or speed up the rate at which it takes to paint a wall, then you can simply assume that each person, working individually, takes 56 minutes to paint 2 walls on their own.

Now knowing this, what can we assume about 2 people painting 2 walls. Obviously the time taken would be cut in half, in this case taking only 28 minutes for those 2 walls. This means one person per wall takes 28 minutes

Now if we have 8 walls and 7 people, we can set up this logical equation:

- One person takes 28 minutes per wall
- One person takes 8 * 28 minutes for 8 walls
- 7 people take (8 * 28)/7 minutes for 8 walls

This gives us that the time taken for 7 people to paint 8 walls to be: 32 minutes

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