A homeowner has hired two individuals to mow his lawn. If person A is able to mow the lawn in 2 hours by himself, and person B is able to mow the lawn in 3 hours by himself, how long would it take for both person A and person B to mow the lawn together?

Rationale

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

This conclusion can be reached by calculating the combined work rate of the two individuals. Person A can complete the task alone in 2 hours, so his work rate is 1 lawn per 2 hours, or 0.5 lawns per hour. Similarly, person B's work rate is 1 lawn per 3 hours, or approximately 0.33 lawns per hour. When working together, their rates add up, which means they can mow approximately 0.83 lawns per hour. Therefore, to mow 1 lawn, it would take them approximately 1.2 hours.

A (5 hours) YOUR ANSWER

This answer would be correct if the work rates of the two individuals were subtractive rather than additive when working together. However, in reality, their work rates add up when they work together, allowing them to complete the task faster than either would individually.

B (1 hour) YOUR ANSWER

This answer would be correct if person A and person B could each mow the lawn in 1 hour. However, their individual rates are slower than this, so even when combined, they cannot complete the task in just 1 hour.

C (2.5 hours) YOUR ANSWER

This answer would be correct if person A and person B were working sequentially, not concurrently. However, the question specifies they are working together which means their combined work rate enables them to complete the task in less time.

D (1.2 hours) CORRECT

This is the correct answer as calculated by adding the work rates of person A and person B. When working together, they can mow 1 lawn in approximately 1.2 hours.

Conclusion

By combining their work rates, person A and person B can mow the lawn together in 1.2 hours. This is less than the time it would take for either of them to complete the task individually. The incorrect answers result from misunderstanding the effects of combined work rates or from inaccurately calculating the combined rate.

A homeowner has hired two individuals to mow his lawn. If person A is able to mow the lawn in 2 hours by himself, and person B is able to mow the lawn in 3 hours by himself, how long would it take for both person A and person B to mow the lawn together?

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

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