SOLUTION: I do not know how to formulate or resolve this problem: (thank you for your help) Joseph takes 15 minutes to do the laundry. Mark takes 4 minutes more to do the laundry by himse

Algebra ->  Equations -> SOLUTION: I do not know how to formulate or resolve this problem: (thank you for your help) Joseph takes 15 minutes to do the laundry. Mark takes 4 minutes more to do the laundry by himse      Log On


   

Question 1006272: I do not know how to formulate or resolve this problem: (thank you for your help)
Joseph takes 15 minutes to do the laundry. Mark takes 4 minutes more to do the laundry by himself than when Joseph and Mark do it together. How much time will it take to Joseph and Mark to do the laundry if they do it together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get
their rate working together
Joseph's rate is:
[ 1 laundry ] / ( 15 min ] = +1%2F15+
-----------------------------
Let +t+ = time in minutes for Mark
and Joseph to do laundry working together
+1%2Ft+ is their rate working together
-----------------------------
Mark's rate when working alone is:
[ 1 laundry ] / [ t + 4 min ] = +1%2F%28+t%2B4+%29+
------------------------------
Add rates of working:
+1%2F15+%2B+1%2F%28+t%2B4+%29+=+1%2Ft+
Multiply both sides by +15%2At%2A%28+t%2B4+%29+
---------------------------------
+t%2A%28+t%2B4+%29+%2B+15t+=+15%2A%28+t%2B4+%29+
+t%5E2+%2B+4t+%2B+15t+=+15t+%2B+60+
+t%5E2+%2B+4t+-+60+=+0+
+%28+t+%2B+10+%29%2A%28+t+-+6+%29+ ( by looking at it )
+t+=+6+ ( time must be positive )
They can do the laundry together in 6 min
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check:
+1%2F15+%2B+1%2F%28+t%2B4+%29+=+1%2Ft+
+1%2F15+%2B+1%2F%286%2B4+%29+=+1%2F6+
+1%2F15+%2B+1%2F10+=+1%2F6+
+4%2F60+%2B+6%2F60+=+10%2F60+
+10%2F60+=+10%2F60+
OK