SOLUTION: tom and huck start a business painting fences. They paint Aunt polly's fence and find that they can paint a 200-ft(2) square .fence in 40min if they work together .If huch works fo

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: tom and huck start a business painting fences. They paint Aunt polly's fence and find that they can paint a 200-ft(2) square .fence in 40min if they work together .If huch works fo      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 833242: tom and huck start a business painting fences. They paint Aunt polly's fence and find that they can paint a 200-ft(2) square .fence in 40min if they work together .If huch works four times faster than tom, how long would it take each of them to paint a 500-ft(2) square fence working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call painting the 200 ft2 fence 1 job
+1%2F40+ = 1 job/40 min
Then a 500 ft2 fence would be 2.5 jobs
Let +R+ = Tom's rate of painting
+4R+ = Huck's rate of painting
-------------------------------
+R+%2B+4R+=+1%2F40+
+5R+=+1%2F40+
+R+=+1%2F200+
+4R+=+1%2F50+
---------------
For Tom:
+R+=+2.5%2Ft+
+1%2F200+=+2.5%2Ft+
+t+=+2.5%2A200+
+t+=+500+
For Huck:
+4R+=+2.5%2Ft+
+1%2F50+=+2.5%2Ft+
+t+=+2.5%2A50+
+t+=+125+
--------------
+500%2F60+=+8+%2B+20%2F60+
Tom takes 8 hrs and 20 min to paint the 500 ft2 fence alone
+125%2F60+=+2+%2B+5%2F60+
Huck takes 2 hrs and 5 min to paint the 500 ft2 fence alone
-----------------
check:
+R+%2B+4R+=+1%2F40+
+1%2F200+%2B+1%2F50+=+1%2F40+
+1%2F200+%2B+4%2F200+=+1%2F40+
+5%2F200++=+1%2F40+
+1%2F40+=+1%2F40+
OK