Question

Working together, two people can cut a large lawn in 4 hr. One person can do the job alone in 1 hr less than the other. How long would it take the faster person to do the job? the faster person would do the job alone in hours.

Answer 1

Answer:The faster person will do the job in 7.53hours

Explanation:

Let t=faster person

Let t-1= the other person

The job to be done =1

Each person will do a fraction of the job

4/t+4/t-1=1

Multiply both sides wit t(t-1)

4(t+1)+4t=t(t-1)

4t+4+4t=t^2+t

8t+4=t^2+t

0=t^2+t-8t-4

t^2-7t-4=0

Use Almighty formular to solve d quadratic equation

X=-b+- rootb^2-4ac/2a

X=t,a=1,b=-7 c=4

Substituting the values you get:

t=-7 +- root 49+16/2

t=-7 +- root 65/2

t=7 +8.06/2=15.06/2

t=7.53 hours