SOLUTION: Tom can whitewash 2/3 of Aunt Polly's fence in 3 hours. Huck can whitewash 1/3 of the fence in 2 hours. If they work together, a) exactly how long will it take Tom and Huck to whit

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Tom can whitewash 2/3 of Aunt Polly's fence in 3 hours. Huck can whitewash 1/3 of the fence in 2 hours. If they work together, a) exactly how long will it take Tom and Huck to whit      Log On


   

Question 1006472: Tom can whitewash 2/3 of Aunt Polly's fence in 3 hours. Huck can whitewash 1/3 of the fence in 2 hours. If they work together, a) exactly how long will it take Tom and Huck to whitewash Aunt Polly's fence? b) What portion of the fence will Huck have whitewashed?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
FENCE per HOUR is the rate unit

Sum of individual rates is their combined rate.
%282%2F3%29%2F3%2B%281%2F3%29%2F2, this combined rate.

2%2F9%2B1%2F6

%282%2F9%29%282%2F2%29%2B%281%2F6%29%283%2F3%29

4%2F18%2B3%2F18

7%2F18, FENCE per HOUR.
This is highlight%2818%2F7=%282%264%2F7%29%2AHOURS%29.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Tom's rate of working is:
[ 2/3 of fence painted ] / [ 3 hrs ]
+%282%2F3%29+%2F+3+=+2%2F9+
-------------------
Huck's rate of working is:
[ 1/3 of fence painted ] / [ 2 hrs ]
+%281%2F3%29+%2F+2+=+1%2F6+
-----------------
Add their rates of painting to get
their rate of painting together
------------------------
Let +t+ = time in hrs for them
to paint fence working together
[ 1 fence painted ] / [ t hrs ] is their
rate working together
--------------------------
+2%2F9+%2B+1%2F6+=+1%2Ft+
Multiply both sides by +18t+
+4t+%2B+3t+=+18+
+7t+=+18+
+t+=+2.571+ hrs
This is about 2 hrs 34 min
----------------------
The portion that Huck paints is:
[ his rate ] x [ time spent painting ]
+%281%2F6%29%2A2.571+=+.4286+
-----------------------
check answer:
+2%2F9+%2B+1%2F6+=+1%2Ft+
+2%2F9+%2B+1%2F6+=+1%2F2.571+
+.2222+%2B+.1667+=+.3889+
+.3889+=+.3889+
OK