# SOLUTION: One roofer can put a neew roof on a house three times faster than another. Working together they can roof a house in 4 days. How long would it take the faster roofer working alone?

Algebra ->  Algebra  -> Percentage-and-ratio-word-problems -> SOLUTION: One roofer can put a neew roof on a house three times faster than another. Working together they can roof a house in 4 days. How long would it take the faster roofer working alone?      Log On

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 Click here to see ALL problems on Percentage-and-ratio-word-problems Question 98406This question is from textbook beginning and intermediate algebra : One roofer can put a neew roof on a house three times faster than another. Working together they can roof a house in 4 days. How long would it take the faster roofer working alone? I need to know how to set up the problem then i can work it from thereThis question is from textbook beginning and intermediate algebra Found 2 solutions by stanbon, checkley71:Answer by stanbon(57361)   (Show Source): You can put this solution on YOUR website!One roofer can put a neew roof on a house three times faster than another. Working together they can roof a house in 4 days. How long would it take the faster roofer working alone? I need to know how to set up the problem then i can work it from there ------------------- 1st roofer DATA: Time = x days/job ; Rate = 1/x job/day ------------------- 2nd roofer DATA: Time = 3x days/job ; Rate = 1/3x job/day --------------- Working-together DATA: Time = 4 day/job ; Rate = 1/4 job/day ------------------ EQUATION: rate + rate = together rate ================ I'll let you solve it. ================= Cheers, Stan H. Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!X*3X/(X+3X)=4 X= THE TIME FOR THE FASTER ROOFER. 3X^2/4X=4 NOW CROSS MULTIPLY 3X^2=16X 3X^2-16X=0 X(3X-16)=0 X=0 A NON ANSWER. 3X-16=0 3X=16 X=16/3 DAYS FOR THE FASTER ROOFER. 3*16/3=16 DAYS FOR THE SLOWER ROOFER. PROOF 16/3*16/(16/3+16=4 (256/3)/[(16+16*3)/3]=4 (256/3)/[(16+48)/3]=4 (256/3)/(64/3)=4 NOW INVERT THE DENOMINATOR & MULTIPLY (256/3)(3/64)=4 CANCEL OUT THE 3s. 256/64=4 4=4