word problem: A janitorial service provides two people to cl

[cptsimose]

Write the Equation and solve

A janitorial service provides two people to clean an office building. Working together, the two can clean the building in five hours. One person is new to the job and would take two hours longer than the other person to clean the building alone. How long (to the nearest tenth) would it take the new worker to clean the building working alone?

 

[Denis]

Re: word problem help!!!!

Write the Equation and solve
A janitorial service provides two people to clean an office building. Working together, the two can clean the building in five hours. One person is new to the job and would take two hours longer than the other person to clean the building alone. How long (to the nearest tenth) would it take the new worker to clean the building working alone?

h = hours alone by experienced guy; so new guy = h + 2

Portion of job in one hour:
1/h + 1/(h + 2)

Since time together = 5 hours:
1/h + 1/(h + 2) = 1/5

Solve for h ; you should get close to 11 hours for new guy.

 

[arthur ohlsten]

let:
R1 = rate one man works at
R2 = rate of second man
w=total work to be done
x equal time it takes first man to do the work

then:
w/[R1+R2]= 5
w/R1=x
w/R2=x+2

find x
w/[R1+R2]=5 divide numerator and denominator by w
1/[R1/w + R2/w]=5
but:
R1/w =1/x and R2/w=1/[x+2] substitute
1/[1/x +1/[x+2] ] =5
1/[ [x+2+x]/x[x+2] ]=5
x[x+2]/[2x+2]=5
x[x+2]= 10x+10
x^2-8x-10=0
x=8+/-[64+40]^1/2 all over 2
x=4 +/- [26]^1/2 CAN NOT HAVE NEGATIVE x
x=4+sqrt26
x=4+5.1
x=9.1 hours answer
x+2= 11.1 hours answer
Arthur

I find it easier to work with rates, than any other approach

 

[Denis]

Ahhh.....beat you by a minute, Arthur :wink: