SOLUTION: Anika and Jazlyn can finish cleaning the house in 2 hours. If it takes Anika working alone 3 hours longer than it takes Jazlyn working alone, how many hours will each girls finis

Algebra ->  Test -> SOLUTION: Anika and Jazlyn can finish cleaning the house in 2 hours. If it takes Anika working alone 3 hours longer than it takes Jazlyn working alone, how many hours will each girls finis      Log On


   

Question 979822: Anika and Jazlyn can finish cleaning the house in 2 hours. If
it takes Anika working alone 3 hours longer than it takes
Jazlyn working alone, how many hours will each girls finish
the work alone?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Basic uniform rates relationship, RT=W, for rate, time, amount of work or task.

PERSON___________________WORK RATE in JOBS/HOURS
Anika____________________1%2F%28x%2B3%29
Jazlyn___________________1%2Fx
Combined_________________1%2F2

Two agents working on the same task simultaneously do so at the sum of their individual rates.

highlight_green%281%2F%28x%2B3%29%2B1%2Fx=1%2F2%29
The rest to do is just arithmetic.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Their rate working together:
[ 1 house cleaned ] / [ 2 hrs ]
--------------------------
Let +t+ = Jazlyn's time working alone in hrs
+t+%2B+3+ = Anika's time working alone in hrs
------------------------------------------
Jazlyn's rate:
[ 1 house cleaned ] / [ t hrs ]
Anika's rate:
[ 1 house cleaned ] / [ t +3 hrs ]
-----------------------------
Add their rates of cleaning to
get their rate cleaning together
+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+1%2F2+
Multiply both sides by +t%2A%28+t%2B3+%29%2A2+
+2%2A%28+t%2B3+%29+%2B+2t+=+t%2A%28+t%2B3+%29+
+2t+%2B+6+%2B+2t+=+t%5E2+%2B+3t+
+t%5E2+-+t+-+6+=+0+
+%28+t-3+%29%2A%28+t%2B2+%29+=+0+
+t+=+3+ ( time must be positive )
and
+t%2B3+=+6+
---------------
Jazlyn's time working alone is 3 hrs
Anika's time working alone is 6 hrs
------------
check:
+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+1%2F2+
+1%2F3+%2B+1%2F6+=+1%2F2+
+2%2F6+%2B+1%2F6+=+3%2F6+
+3%2F6+=+3%2F6+
OK