IT takes chris 9 hours longer to construct a fence than it take tony. If they work together, they caan construct the fence in 20
hours. How long would it take each man working alone?
2 answers:
Answer:
Tony = 36 Hours
Chris = 45 Hours
Step-by-step explanation:
let y+9 = Chris's time to build the fence alone
let y = Tony's time
let the completed job = 1
20/y+9 + 20/y = 1
Multiply the equation by y(y+9)
20y + 20(y+180) = y(y+9)
20y + 20y + 180 = y^2 + 9y
40 y + 180 = y^2 + 9y
0 = y^2 + 9y -40y - 180
y^2 - 31y - 180
(y + 5)(y - 36) = 0
y + 5 = 0
y = 0 - 5
y = -5 We reject this answer since we're only interested in the positive answer in terms of work done by two people.
y - 36 = 0
y = 0 + 36
y = 36 hours
So Chris takes y + 9 hours more than Tony
Chris's Time = y + 9
Chris's Time = 36 + 9
Chris's Time = 45 hours
ANSWER
Tony: 36 hours
Chris: 45 hours
EXPLANATION
If it takes Tony x hours to construct the fence, then it will take Chris (x+9) hours.
Tony's rate is

Chris' rate is

Their combined rate in terms of x is

Their combined rate must equal

This implies that;


Cross multiply,

Expand;

This implies that,





We discard the negative value.
Hence

Therefore it will take Tony 36 hours and Chris 45 hours.
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