Right Answer Explanation / Suggested Answer :
Let x be the number of hours Alex and Jordan take to complete the project when working together.
Alex's time alone: x + 12 hours
Jordan's time alone: x + 27 hours
The rate at which Alex works alone is projects per hour, and the rate at which Jordan works alone is projects per hour.
Working together, their combined rate is projects per hour.
The equation for their combined rates is:
x(x + 27) + x(x + 12) = (x + 12)(x + 27)
x2 + 27x + x2 + 12x = x2 + 39x + 324
2x2 + 39x = x2 + 39x + 324
x2 = 324
x = = 18
Alex and Jordan take 18 hours to complete the project when working together.
Amity007
Alex and Jordan are two experienced carpenters who often collaborate on major construction projects. This time, they are tasked with building a custom wooden deck for a large home. Individually, Alex takes 12 hours longer, and Jordan takes 27 hours longer to complete the project than they would have taken if they worked as a team. How many hours do Alex and Jordan take to complete the project when working together?
(Source=TCYOnline)
A. 10 hours
B. 14 hours
C. 18 hours
D. 20 hours
E. 28 hours