SOLUTION: Mark can mow a lawn in 20 minutes less time than his sister Marie. Together they can mow the lawn in 24 minutes. How long will it take Marie to finish the mowing if she works alone

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Mark can mow a lawn in 20 minutes less time than his sister Marie. Together they can mow the lawn in 24 minutes. How long will it take Marie to finish the mowing if she works alone      Log On


   

Question 909186: Mark can mow a lawn in 20 minutes less time than his sister Marie. Together they can mow the lawn in 24 minutes. How long will it take Marie to finish the mowing if she works alone?
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Marie's rate of mowing is:
( 1 lawn mowed ) / ( t minutes )
Mark's rate of mowing is:
( 1 lawn mowed ) / ( t - 20 minutes )
Working together, their rate is:
( 1 lawn mowed ) / ( 24 minutes )
-------------------------------
Add their rates of mowing to get
their rate mowing together
+1%2Ft+%2B+1%2F%28+t-20+%29+=+1%2F24+
Multiply both sides by +t%2A%28+t-20+%29%2A24+
+24%2A%28+t-20+%29+%2B+24t+=+t%2A%28+t-20+%29+
+24t+-+480+%2B+24t+=+t%5E2+-+20t+
+t%5E2+-+68t+%2B+480+=+0+
You can complete the square:
+t%5E2+-+68t+%2B+%28+68%2F2+%29%5E2+=+%28+68%2F2+%29%5E2+-+480+
+t%5E2+-+68t+%2B+1156+=+1156+-+480+
+t%5E2+-+68t+%2B+1156+=+676+
+%28+t+-+34+%29%5E2+=+26%5E2+
+t+-+34+=+26+
+t+=+60+
another solution is:
+t+-+34+=+-26+
+t+=+8+
I can't use this solution, since that would mean Marie
working alone could mow faster than both mowing together
------------------
Marie, working alone, can mow the lawn in 60 min
check:
+1%2Ft+%2B+1%2F%28+t-20+%29+=+1%2F24+
+1%2F60+%2B+1%2F%28+60-20+%29+=+1%2F24+
+1%2F60+%2B+1%2F40+=+1%2F24+
+1%2F15+%2B+1%2F10+=+1%2F6+
Multiply both sides by +30+
+2+%2B+3+=+5+
+5+=+5+
OK

Answer by richwmiller(17219) About Me  (Show Source):