Working together Katherine and Julianna can plant new trees on there recently divorced land in 4 days working alone it would take Giuliana to days longer than it would take Catherine to plant the trees how long would it take Katherine working alone to plant the trees

The rates of each working together are added

Two people = 1/4

One person = 1 / x + 2

The other person = 1 / x

Solve for x and you can find other person’s rate:

1 / x + 1 / x + 2 = 1 / 4

x = 3 + (sqrt17), 3 - (sqrt17)

x = 7.21

the other solution would be:

Let t be the time necessary by the 1st person to do the job alone

then

(t + 2) is the time required by the 2nd person alone

Let the completed job = 1

A classic work equation:

Each person will do a fraction of the job, the two fractions add up to 1

4 / t + 4 / t + 2 = 1

multiply by t (t+2), results

4 (t+2) + 4t = t (t+2)

4t + 8 + 4t = t^2 + 2t

Arrange them as a quadratic equation

t^2 + 2t - 8t - 8

t^2 - 6t - 8 = 0

then use the quadratic equation, the answer will be 7.21.

It will take Katherine approximately 7 days working alone to plant the trees.