Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completes half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Jose take to complete the task if if he worked alone? Assume that Jane is more efficient than Jose?
Please show ALL work
No answer choices?
Let Jose finish work in x days and Jane in y days. So to finish half task jose will take x/2 days and Jane will take y/2 days.
By given info we have x/2 + y/2 = 45 or (x + y) = 90 ---(1)---
Also when both work together we have 1/x + 1/y = 1/20
or (x+y)/xy = 1/20
0r xy = 20 * (x + y) = 1800
Since jane is efficient this means x > y
we know (x - y)^2 = (x + y)^2 - 4xy
or (x - y)^2 = 8100 - 7200 = 900
or x - y = 30
Since x + y = 45 on solving we get x = 75/2 = 37.5 and y is 7.5