Question

Team one needs 5 days to finish the project by themselves, team two needs 6 days to finish it by themselves. If the two teams work together, how many days are needed?

a) 2.4 days
b) 2.5 days
c) 2.6 days
d) 2.7 days

Answer 1

When team one and team two work together, they have a combined rate of (11/30) of the project per day, which means they would complete the project in approximately 2.73 days, with the nearest answer choice being 2.7 days.

Step-by-step explanation:

To calculate the total time needed for two teams working together, we can use the rates at which each team works. Team one completes the project in 5 days, which means their rate of work is 1 project per 5 days, or 1/5 of the project per day. Team two completes the project in 6 days, meaning their rate is 1 project per 6 days, or 1/6 of the project per day. When they work together, their combined rate is 1/5 + 1/6 per day. To find this sum, we need a common denominator, which in this case is 30 (5 × 6).

Combining the rates of the two teams gives us (6/30) + (5/30) = (11/30) of the project per day. To find the total number of days (D) needed to complete one entire project working together at this combined rate, we set up the equation D × (11/30) = 1. Solving for D gives us D = 30/11, which is approximately 2.73 days. Thus, the closest answer is d) 2.7 days.