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?

Suppose every brick-layer works at the same rate. 
<pre>
Let the rate of 1 brick-layer be R in walls per day.

Then 

(rate)(time) = (fraction of wall completed) 
</pre>
Five brick-layers working together can build a wall in 20 days. 
<pre>
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.
</pre>
Three brick-layers work on the wall for 10 days... 
<pre>
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.
</pre>
...before eleven more brick-layers join them. 
<pre>
That makes 14 brick-layers  

The rate of 1 brick-layer is 1/100 so the rate of 14 
brick-layers is 14/100
</pre>
How much longer will it take them to finish the wall?
<pre>
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</pre>