Question 16

Both person A and person B would take 1.2 hours to mow the lawn together.

When working together, person A and person B can complete the task in 1.2 hours. This is derived from their individual work rates, which combine to make the mowing process more efficient.

A) 5 hours

This option is incorrect because if both individuals took 5 hours to mow the lawn together, it would imply that their combined work rate is significantly lower than their actual capabilities. Given their individual times of 2 and 3 hours, they would complete the task much faster than 5 hours.

B) 1 hour

Option B is incorrect as well since it suggests that they could finish mowing the lawn in just 1 hour. This would require both individuals to work at a combined rate that exceeds their actual work rates, which is not feasible based on the provided information.

C) 2.5 hours

While this option seems plausible, it is also incorrect. The combined efforts of person A and person B would reduce the time it takes to mow the lawn to less than 2.5 hours, given that their work rates would allow them to finish the job quicker than this estimate.

D) 1.2 hours

This is the correct option. By calculating the individual work rates of both individuals (1/2 for person A and 1/3 for person B), the combined work rate becomes 5/6 of the lawn per hour. Therefore, the time taken to complete the lawn together is 1 divided by the combined work rate, resulting in 1.2 hours.

Conclusion

The correct answer of 1.2 hours accurately reflects the combined efficiency of both workers. The other options fail to account for the effective collaboration between person A and person B, leading to an underestimation of their combined capabilities. Thus, 1.2 hours is definitively the correct solution based on their individual mowing times.