SOLUTION: Danny and Rennan can do a piece of work in 6 days. How long will it take each of them to finish the work alone, if Danny can work 3/2 as fast as Rennan.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Danny and Rennan can do a piece of work in 6 days. How long will it take each of them to finish the work alone, if Danny can work 3/2 as fast as Rennan.      Log On


   

Question 1111104: Danny and Rennan can do a piece of work in 6 days. How long will it take each of them to finish the work alone, if Danny can work 3/2 as fast as Rennan.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Rennan's rate r
Danny's rate (3/2)r
Together, one job in 6 days: r%2B%283%2F2%29r=1%2F6

r=1%2F15--------Rennan can do one job in 15 days.
%283%2F2%29r=%283%2F2%29%2A%281%2F15%29=1%2F10-------Danny would need 10 days to do same job.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R+ = Rennan's rate of working
+%283%2F2%29%2AR+ = Danny's rate of working
+1%2F6+ = their rate working together
-------------------------------------
Add their individual ratyes to get their rate
working together
+R+%2B+%283%2F2%29%2AR+=+1%2F6+
Multiply both sides by +2+
+2R+%2B+3R+=+1%2F3+
+5R+=+1%2F3+
+R+=+1%2F15+
and
+%283%2F2%29%2AR+=+%283%2F2%29%2A%281%2F15%29+
+%283%2F2%29%2AR+=+1%2F10+
-------------------------------
Rennan takes 15 days working alone
Danny takes 10 days working alone
---------------------------------------
chck:
+R+%2B+%283%2F2%29%2AR+=+1%2F6+
+1%2F15+%2B+1%2F10+=+1%2F6+
+2%2F30+%2B+3%2F30+=+5%2F30+
+5%2F30+=+5%2F30+
OK