SOLUTION: It takes Ralph 6 hours to paint a fence alone. Lisa can do the same job in 9 hours. If Ralph paints alone for 45 minutes before Lisa begins helping, how long must they work togethe

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Question 906514: It takes Ralph 6 hours to paint a fence alone. Lisa can do the same job in 9 hours. If Ralph paints alone for 45 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer as a simplified fraction.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
You asked another one like this in which only two of the values were different but the description and question were the same.

1 job is "paint the fence"

RATES in jobs per hours
Ralph, 1%2Fm
Lisa, 1%2Ff

Both questions used 45 minutes for the time that Ralph (m for male) painted alone; which is
3%2F4 hour. Let x be the time that Ralph and Lisa (f for female) work together after
Ralph worked alone.

highlight_green%28%281%2Fm%29%283%2F4%29%2B%281%2Fm%2B1%2Ff%29x=1%29, accounting for ONE WHOLE JOB.
One equation, three variables, but m and f are to be used as known constants, and only
x is the unknown variable to be solved. Solve for x.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Ralph's rate of painting is:
( 1 fence ) / ( 6 hrs ), or
+1%2F6+
-----------
+45+ min = +3%2F4+ hr
the fraction of the whole job that
Ralph does in +3%2F4+ hr is:
+%283%2F4%29%2A%281%2F6+%29+=+1%2F8+
That means that +7%2F8+ of
the job remains
--------------------
They both now work together
Let +t+ = time in hrs for them to finish
+1%2F6+%2B+1%2F9+=+%28%287%2F8%29%29+%2F+t+
+1%2F6+%2B+1%2F9+=+7+%2F+%28%288t%29%29+
Multiply both sides by +72t+
+12t+%2B+8t+=+63+
+20t+=+63+
+t+=+63%2F20+
It will take them 63/20 hrs to finish painting
check:
+1%2F6+%2B+1%2F9+=+%28%287%2F8%29%29+%2F+t+
+1%2F6+%2B+1%2F9+=+%28%287%2F8%29%29+%2F+%28%2863%2F20%29%29+
+1%2F6+%2B+1%2F9+=+%287%2F8%29%2A%28+20%2F63%29+
+1%2F6+%2B+1%2F9+=+20%2F72+
+1%2F6+%2B+1%2F9+=+5%2F18+
+3%2F18+%2B+2%2F18+=+5%2F18+
+5%2F18+=+5%2F18+
OK