SOLUTION: mike can clean a backyard twice as fast as jill. jill takes one hour longer than john to clean the same backyard.john cleans the backyard in three hours. how long will it take all

Algebra ->  Rate-of-work-word-problems -> SOLUTION: mike can clean a backyard twice as fast as jill. jill takes one hour longer than john to clean the same backyard.john cleans the backyard in three hours. how long will it take all       Log On


   

Question 525519: mike can clean a backyard twice as fast as jill. jill takes one hour longer than john to clean the same backyard.john cleans the backyard in three hours. how long will it take all three to clean the yard together?
leave the answer in simplest fractional terms.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = Jill's time to clean backyard
given:
+t%2F2+ = Mike's time to clean a backyard
+t+-+1+=+3+ = John's time to clean a backyard
Let +q+ = time with all 3 working
----------------
+t+-+1+=+3+
+t+=+4+
Add their rates of working to get rate working together
+1%2Ft+%2B+1%2F%28t%2F2%29+%2B+1%2F%28t-1%29+=+1%2Fq+
+1%2F4+%2B+1%2F2+%2B+1%2F3+=+1%2Fq+
Multiply both sides by 12q+
+3q+%2B+6q+%2B+4q+=+12+
+13q+=+12+
+q+=+12%2F13+
It will take all three 12/13 hr
( this is about 55 min and 23 sec )

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

mike can clean a backyard twice as fast as jill. jill takes one hour longer than john to clean the same backyard.john cleans the backyard in three hours. how long will it take all three to clean the yard together?
leave the answer in simplest fractional terms.

John can clean the yard in 3 hours, or 1%2F3 of yard in 1 hour
Jill can clean it in 4 (3 + 1) hours, or ¼ of yard in 1 hour
Mike can clean it in 2 (4 * ½) hours, or 1%2F2 of yard in 1 hour


%28%281%2F3%29+%2B+%281%2F4%29+%2B+%281%2F2%29%29%2F1+=+%281%2FT%29, with T being amount of time, in hours

%28%284+%2B+3+%2B+6%29%2F12%29%2F1+=+%281%2FT%29

%28%2813%2F12%29%2F1%29+=+%281%2FT%29

%2813T%2F12%29+=+1 ------- Cross-multiplying

13T = 12 ------- Cross-multiplying

T, or time taken by all 3 to clean the yard = highlight_green%2812%2F13%29 hr

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