SOLUTION: A takes half time than B to do a work. C takes time equal to A and B together. If three together can do the work in 7 days then in how many days A alone can do the work?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A takes half time than B to do a work. C takes time equal to A and B together. If three together can do the work in 7 days then in how many days A alone can do the work?      Log On


   



Question 959538: A takes half time than B to do a work. C takes time equal to A and B together. If three together can do the
work in 7 days then in how many days A alone can do the work?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = number of days for A to
do the work working alone
--------------------------
B takes twice as long to do the work, so
+2d+ = number of days for B to
do the work working alone
--------------------------
C takes time equal to A and B together, so
+d+%2B+2d+=+3d+ = number of days for C to
do the work working alone
---------------------------
A, B, and C together take +7+ days
to do the work
--------------
Add their rates of working to get
their rate working together
------------------------
+1%2Fd+%2B+1%2F%282d%29+%2B+1%2F%283d%29+=+1%2F7+
Multiply both sides by +42d+
+42+%2B+21+%2B+14+=+6d+
+6d+=+77+
+d+=+12.8333+
+2d+=+25.+667+
+3d+=+38.5+
----------------
A takes 12.8333 days working alone
B takes 25.667 days working alone
C takes 38.5 days working alone
---------------------------------
check:
+1%2Fd+%2B+1%2F%282d%29+%2B+1%2F%283d%29+=+1%2F7+
+1%2F12.8333+%2B+1%2F25.667+%2B+1%2F38.5+=+1%2F7+
+.0779223+%2B+.03896099+%2B+.025974+=+.142857+
+.142857+=+.142857+
OK