A and B can complete a job together in 18 days; A alone takes 30 days. They worked together some days, then A left; B finished the rest. The total time was 20 days. For how many days did they work together?
Show answer & explanation
Correct answer: A
Explanation
Given:
A + B = 18 days
A = 30 days
Total time = 20 days
According to the formula:
Work Rate = 1 / Time
Rate of (A + B) = 1/18
Rate of A = 1/30
Rate of B = 1/18 − 1/30
= (5 − 3)/90 = 2/90 = 1/45
Let the time worked together be x days.
x(1/18) + (20 − x)(1/45) = 1
x/18 + (20 − x)/45 = 1
Multiplying by the LCM (90):
5x + 2(20 − x) = 90
5x + 40 − 2x = 90
3x = 50
x = 16⅔ days