algebra word problem?

Question

Working together, two people can complete at task in 5 hours. Working alone, one person takes two hours longer than the other. How long would it take each person to do the task alone?

Answer 1

This type of problem is solved by finding the fraction of the job each, then both, can do in an hour. If t = the hours for the faster person, she can do 1/t of the job in an hour, the slower can do 1/(t+2) of the job, and together they do 1/5 of the job in an hour.

So 1/t + 1/(t+2) = 1/5

Answer 2

Person A takes 4 hours for working alone
Person B takes 6 hours for working alone

Together they take 6+4=10/2=5 hours.

Answer 3

It can be solved by finding the fraction of the job each can do in hour
suppose i can do some work in 10 hrs ,then i will complete 1/10 of it in 1hr.
similarly let us suppose
If x = the hours for the faster person, he can do 1/x of the work in an hour.
The slower can do 1/(x+2) of the work in an hr, and together they do 1/5 of the work in an hour.

So 1/x + 1/(x+2) = 1/5
i.e (2x+2)/(x*(x+2))=1/5
10x+10=x^2 + 2x
x^2 -8x-10=0
x =9.099 (other x is '-'ve therefore ignore it)
so faster person will take 9.099 hrs &
slower will take 11.099 hrs

Answer 4

Let the people be 'x' and 'y'
x = y + 2.....Eq 1
x + y = 5.....Eq 2
Taking Eq 1 and substituting the value of 'x' in Eq 2
y + 2 + y = 5
2y = 3
y = 3/2
y = 1.5
y takes 1.5 hours to finish the work
x = y + 2
= 1.5 + 3
= 3.5
x takes 3.5 hours to finish the work
check the answer.

Answer 5

Let the people be 'x' and 'y'
x = y + 2.....Eq 1
x + y = 5.....Eq 2
Taking Eq 1 and substituting the value of 'x' in Eq 2
y + 2 + y = 5
2y = 3
y = 3/2
y = 1.5
y takes 1.5 hours to finish the work
x = y + 2
= 1.5 + 3
= 3.5
x takes 3.5 hours to finish the work

Answer 6

Let the people be 'x' and 'y'
x = y + 2.....Eq 1
x + y = 5.....Eq 2
Taking Eq 1 and substituting the value of 'x' in Eq 2
y + 2 + y = 5
2y = 3
y = 3/2
y = 1.5
y takes 1.5 hours to finish the work
x = y + 2
= 1.5 + 3
= 3.5
x takes 3.5 hours to finish the work

Answer 7

let one person do the work in x hours
other will do in x+2 hours
both together do in 5 hours
work done by one in one day=1/x
work done by other in one day=1/(x+2)
work done by both in one day=1/5

thus 1/x+1/(x+2)=1/5
==> x+2 + x= x(x+2)/5
==> 10x+10 = x^2+2X
==> x*2-8x-10=0
_____
x= [ -(-8)+\/64+40]/2 =9 approx..

thus they will individually take 9 and 11 hours approx...