SOLUTION: please help I don't know how to set up an equation to solve this problem Brian takes 2 hours longer to complete a job than Shane. If they can complete the job together in 5 hour

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Question 768485: please help I don't know how to set up an equation to solve this problem
Brian takes 2 hours longer to complete a job than Shane. If they can complete the job together in 5 hours, find how long it takes each person to complete the job alone.
?????
1/x+1/(x+2)=x ??? this is what I tried

Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates job-completion problem,
Let x = time for Shane to do one job; his rate is 1/x jobs per hour.
Then 2+x = time in hours for Brian to do the same job; which is 1/(x+2) job per hour.
THEY work together for 5 hours.
Let h = 5 hours.

Note, the description of the problem implied that Brian and Shane worked together and did ONE job.

Use the fundamental concept of rate.
(jobs/time)=(jobs)/(time)
r=j%2Ft__________ r is rate, j is amount of jobs, t is time.

USE THE FUNDAMENTAL CONCEPT OF UNIFORM RATE:
highlight%28%281%2Fx%2B1%2F%28x%2B2%29%29%2Ah=1%29
That IS {rate}*{time}={job}. Their rates are additive while they work together. They do ONE job, shown as 1.

SYMBOLIC SOLUTION PROCESS:
Just substitute 5 for h, and solve the equation for x. Tell if you have trouble with doing this. Most of the analyzing and solution process is to obtain the equation highlighted.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Shane's time in hrs
to complete job working alone
+t+%2B+2+ = Brian's time to complete
job working alone
------------------
Shane's rate of working:
( 1 job done ) / ( t hrs )
Brian's rate of working:
( 1 job done ) / ( t + 2 hrs )
Their rate working together:
( 1 job done ) / ( 5 hrs )
----------------------
Add their rates to get their rate working together
+1%2Ft+%2B+1%2F%28+t+%2B+2+%29+=+1%2F5+
Multiply both sides by +t%2A%28+t+%2B+2+%29%2A5+
+5%2A%28+t+%2B+2+%29+%2B+5t+=+t%2A%28+t+%2B+2+%29+
+5t+%2B+10+%2B+5t+=+t%5E2+%2B+2t+
+-t%5E2+%2B+8t+%2B+10+=+0+
Using quadratic formula:
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+8+
+c+=+10+
+t+=+%28-8+%2B-+sqrt%28+8%5E2+-+4%2A%28-1%29%2A10+%29%29+%2F+%282%2A%28-1%29%29+
+t+=+%28-8+%2B-+sqrt%28+64+%2B+40+%29%29+%2F+%28+-2+%29+
+t+=+%28-8+%2B-+sqrt%28++104+%29%29+%2F+%28+-2+%29+
+t+=+%28+-8+-+10.2+%29+%2F+%28+-2+%29+
+t+=+18.2+%2F+2+
+t+=+9.1+
+t+%2B+2+=+11.1+
Note that using the positive square root gives me
a negative answer for time, so I used the negative
square root
Working alone, Shane takes 9.1 hrs
Brian takes 11.1 hrs
------------------
check:
+1%2Ft+%2B+1%2F%28+t+%2B+2+%29+=+1%2F5+
+1%2F9.1+%2B+1%2F11.1+=+.2+
+.11+%2B+.09+=+.2+
+.2+=+.2+
OK