SOLUTION: Five brick-layers working together can build a wall in 20 days. Suppose every brick-layer works at the same rate. Three brick-layers work on the wall for 10 days before eleven m

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Question 1036207: Five brick-layers working together can build a wall in 20 days.
Suppose every brick-layer works at the same rate. Three
brick-layers work on the wall for 10 days before eleven more
brick-layers join them. How much longer will it take them to
finish the wall?
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
in one day, 5 brick layers build 1/20 of a wall, so each one does 1/100 of a wall per day.
Three brick layers at 10 days do 30% of the wall.
therefore 11 more brick layers join them and there are 14 brick layers available, each of whom can build 1/100 of the wall. In each day, 14/100 of the wall will be done, and in 5 days, 70% of the wall will be done, finishing it.
Five days.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Five brick-layers working together can build a wall in 20 days.
Suppose every brick-layer works at the same rate. Three
brick-layers work on the wall for 10 days before eleven more
brick-layers join them. How much longer will it take them to
finish the wall?
Suppose every brick-layer works at the same rate. 
Let the rate of 1 brick-layer be R in walls per day.

Then 

(rate)(time) = (fraction of wall completed)

Five brick-layers working together can build a wall in 20 days. 
The rate of 1 brick-layer is R so the rate of 5 
brick-layers is 5R

(rate)(time) = (fraction of wall completed),so

(5R)(20) = 1
    100R = 1
       R = 1/100 of a wall per day.

Three brick-layers work on the wall for 10 days... 
The rate of 1 brick-layer is 1/100 so the rate of 3 
brick-layers is 3/100

(rate)(time) = (fraction of wall completed)
(3/100)(10)  = 3/10 of the wall completed

So there's still 7/10 of the wall left to go.

...before eleven more brick-layers join them. 
That makes 14 brick-layers  

The rate of 1 brick-layer is 1/100 so the rate of 14 
brick-layers is 14/100

How much longer will it take them to finish the wall?
Let the answer be x days for the 14 to finish the remaining 
7/10 of the wall.

(rate)(time) = (fraction of wall completed)

(14/100)(x)  = 7/10 

Multiply both sides by 100

14x = 70

x = 5 more days.

Edwin
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