How long would it take​ Katherine, working​ alone, to plant the​ trees?

Question

Working​ together, Katherine and Julianna can plant new trees on their recently deforested land in 8 days. Working​ alone, it would take Julianna 3 days longer than it would take Katherine to plant the trees. How long would it take​ Katherine, working​ alone, to plant the​ trees?

It would take about ___ days for Katherine to plant the trees alone.

Answer 1

If Katharine takes k days to plant the trees, Katharine's rate of tree planting is 1/k

As it takes Julianne 3 days longer, her rate is 1/(k+3)

Then, their combined rate is 1/k + 1/(k+3)

As it takes them 8 days together, their combined rate is 1/8

Then, 1/k + 1/(k+3) = 1/8

((k+3)+k)/(k(k+3)) = 1/8

8(2k+3) = k^2 + 3k

k^2 - 13k - 24 = 0

k = (13 ± √265)/2

k = 14.6394102980499

(The negative solution is thrown out)

Round k as you wish.

Note that 1/(k) + 1/(k+3) = 1/8.