|
Question 313753: A building contractor employs a master mason, a journeyman mason and an apprentice mason.
The master mason and the journeyman working together can finish a brick wall in 10 hours. It
takes the master and apprentice 12 hours to do the same job, while the journeyman and apprentice
require 15 hours to complete the task.
If all three work together, how long does it take to build the wall?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A building contractor employs a master mason, a journeyman mason and an apprentice mason.
The master mason and the journeyman working together can finish a brick wall in 10 hours.
It takes the master and apprentice 12 hours to do the same job,
while the journeyman and apprentice require 15 hours to complete the task.
:
Find how many hrs each require working alone
:
Let the individual times of the three masons be: m, j, a
:
Let the completed job = 1
:
Write an equation for each statement:
:
"The master mason and the journeyman working together can finish a brick wall in 10 hours"
Eq1: +  = 1
:
"It takes the master and apprentice 12 hours to do the same job,"
Eq2: +  = 1
:
"the journeyman and apprentice require 15 hours to complete the task."
Eq3: +  = 1
:
Multiply Eq1 by 6 and Eq2 by 5:
 +  = 6
+  = 5
-------------------------------Subtraction eliminates m, so we have
- = 1
:
Multiply eq3 by 4 and add to the above equation
- = 1
+ = 4
----------------------------- adding eliminates a, find j
 = 5
5j = 120
j = 
j = 24 hrs to do the job alone
:
Substitute 24 for j in eq1, find m
+  = 1
Multiply by 24m
10(24) + 10m = 24m
240 = 24m - 10m
m = 
m = 17.14 hrs to do the job alone
:
Using eq3, find a
 + = 1
Multiply by 24a
15a + 15(24) = 24a
360 = 24a - 15a
a = 
a = 40 hrs to do the job alone
:
Summarize: a = 40; j = 24; m = 17.14 hrs
:
"If all three work together, how long does it take to build the wall?"
Let t = time required when all three work together
 +  +  = 1
multiply equation by 17.14*24*40 = 16454.4, results:
960t + 685.6t + 411.36t = 16454.4
2056.96t = 16454.4
t = 
t ~ 8 hrs all three working
;
:
Check solution using a calc:
8/17.14 + 8/24 + 8/40 =
.467 + .333 + .2 = 1
|
|
|
| |
