SOLUTION: A B and C can clean a house in 2 hours A can clean a house in 5 hours B can clean a house in 6 hours How long does it take A and C to clean a house? My work so far: A= 300/6

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: A B and C can clean a house in 2 hours A can clean a house in 5 hours B can clean a house in 6 hours How long does it take A and C to clean a house? My work so far: A= 300/6      Log On


   

Question 1058019: A B and C can clean a house in 2 hours
A can clean a house in 5 hours
B can clean a house in 6 hours
How long does it take A and C to clean a house?
My work so far:
A= 300/60 min.
B= 360/60
C= x/60

Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Their rates of cleaning would look like:
[ 1 house cleaned ] / [ time to clean the house ]
Let +R%5Ba%5D+ = A's rate of cleaning
Let +R%5Bb%5D+ = B's rate of cleaning
Let +R%5Bc%5D+ = C's rate of cleaning
-----------------------------------
given:
(1) +R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F2+
(2) +R%5Ba%5D+=+1%2F5+
(3) +R%5Bb%5D+=+1%2F6+
-------------------------------
By substitution:
(1) +1%2F5+%2B+1%2F6+%2B+R%5Bc%5D+=+1%2F2+
Multiply both sides by +30+
(1) +6+%2B+5+%2B+30R%5Bc%5D+=+15+
(1) +30R%5Bc%5D+=+4+
(1) +R%5Bc%5D+=+2%2F15+
----------------------
Let +t+ = time in hrs for A and C together to
clean a house
+1%2F5+%2B+2%2F15+=+1%2Ft+
Multiply both sides by +15t+
+3t+%2B+2t+=+15+
+5t+=+15+
+t+=+3+
A and C together will take 3 hrs to clean a house
----------------------
check answer:
Plug this result into (1)
(1) +R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F2+
(1) +%28+R%5Ba%5D+%2B+R%5Bc%5D+%29+%2B+R%5Bb%5D+=+1%2F2+
(1) +1%2F3+%2B+1%2F6+=+1%2F2+
(1) +2%2F6+%2B+1%2F6+=+3%2F6+
(1) +3%2F6+=+3%2F6+
OK


Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
I see that in solving joint work problems you are in very starting position.

There are introductory lessons on solving joint-work problems with detailed explanations in this site
    - Using Fractions to solve word problems on joint work,
    - Solving more complicated word problems on joint work,
    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".