SOLUTION: The first worker can make 5 chairs in 3 hours. The second worker can make 7 chairs in 4 hours. How long will it take the two workers to manufacture 10 chairs? Don't forget to

Question 895890: The first worker can make 5 chairs in 3 hours.
The second worker can make 7 chairs in 4 hours.
How long will it take the two workers to manufacture 10 chairs? Don't forget to show units.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Letx=amount of time needed for the two workers to make 10 chairs
The first worker works at the rate of 5/3=1.67 chairs per hour
The second worker works at the rate of 7/4=1.75 chairs per hour
Together they work at the rate of (5/3) + (7/4)=(20/12)+(21/12)=(41/12)=3.42 chairs per hour. So, our equation to solve is:
3.42x=10
x=2.92 hours time needed for the two workers to make 10 chairs working together
CK
In 2.92 hours, the first worker makes (1.67)(2.92)=4.88 chairs
In 2.92 hours, the second worker makes (1.75)(2.92)=5.11 chairs
Together they make 4.88+5.11=9.99 chairs
Instead of 10, we got 9.99 and this is caused by round-off errors.
If we work it out in fractions, we should get the exact answer. Lets try it:
Together, they work at the rate of 41/12 chairs per hour
So our equation to solve is:
(41/12)x=10 multiply each side by 12
41x=`120
x=120/41 hours
CK
In 120/41 hours, the first worker makes (5/3)(120/41)=200/41 chairs
In 120/41 hours, the second worker makes (7/4)(120/41)=210/41 chairs
200/41 +210/41=410/41=10 chairs YEA!!!!
Hope this helps---ptaylor
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