SOLUTION: To finish construction at a site, it would take 4 bulldozers and 3 shovels 2 days, and it take 5 bulldozers and 1 shovel 3 days. How many days does it take 1 bulldozers and 1 shove

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: To finish construction at a site, it would take 4 bulldozers and 3 shovels 2 days, and it take 5 bulldozers and 1 shovel 3 days. How many days does it take 1 bulldozers and 1 shove      Log On


   

Question 903859: To finish construction at a site, it would take 4 bulldozers and 3 shovels 2 days, and it take 5 bulldozers and 1 shovel 3 days. How many days does it take 1 bulldozers and 1 shovel?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the construction 1 job
--------------------------
Let +R%5B1%5D+ = the rate of working
of a bulldozer in jobs / hour
--------------------------
Let +R%5B2%5D+ = the rate of working
of a shovel in jobs / hour
--------------------------
(1) +4R%5B1%5D+%2B+3R%5B2%5D+=+1%2F2+
(2) +5R%5B1%5D+%2B+1%2AR%5B2%5D+=+1%2F3+
--------------------------
Multiply both sides of (2) by +3+
and subtract (1) from (2)
(2) +15R%5B1%5D+%2B+3R%5B2%5D+=+1+
(1) +-4R%5B1%5D+-+3R%5B2%5D+=+-1%2F2+
---------------------------
+11R%5B1%5D+=+1%2F2+
+R%5B1%5D+=+1%2F22+
and
(2) +5R%5B1%5D+%2B+1%2AR%5B2%5D+=+1%2F3+
(2) +5%2F22+%2B+1%2AR%5B2%5D+=+1%2F3+
(2) +R%5B2%5D+=+1%2F3+-+5%2F22+
(2) +R%5B2%5D+=+22%2F66+-+15%2F66+
(2) +R%5B2%5D+=+7%2F66+
---------------------
+R%5B1%5D+%2B+R%5B2%5D+=+1%2Ft+
+3%2F66+%2B+7%2F66+=+1%2Ft+
+10%2F66+=+1%2Ft+
+t+=+66%2F10+
+t+=+6.6+ days
------------------
It takes 1 bulldozer and 1 shovel 6.6 days
check:
(1) +4R%5B1%5D+%2B+3R%5B2%5D+=+1%2F2+
(1) +4%2A%283%2F66%29+%2B+3%2A%287%2F66%29+=+1%2F2+
(1) +12%2F66+%2B+21%2F66+=+33%2F66+
(1) +33%2F66+=+33%2F66+
------------------------
(2) +5R%5B1%5D+%2B+1%2AR%5B2%5D+=+1%2F3+
(2) +5%2A%283%2F66%29+%2B+1%2A%287%2F66%29+=+1%2F3+
(2) +15%2F66+%2B+7%2F66+=+22%2F66+
(2) +22%2F66+=+22%2F66+
Ok
Hope I got it