A gardener takes 3 hours to water a lawn. If sprinklers are installed and water 60% of the area in 2 hours, how long does it take to complete the job if both work together?
Correct answer: C. 1.8 hrs
- A. 1.2 hrs
- B. 1.5 hrs
- C. 1.8 hrs
- D. 2 hrs
Explanation
To solve this problem, start by determining the work rate of each party. The gardener can complete the entire lawn in 3 hours, so his rate is 1/3 of the lawn per hour. The sprinklers cover 60% of the lawn in 2 hours, translating to a rate of 0.6/2 = 0.3 of the lawn per hour. Adding these rates gives a combined work rate of 1/3 + 0.3 = 0.6333 (or approximately 0.63) of the lawn per hour. To find the total time taken to water the entire lawn together, divide 1 by their combined work rate: 1 / 0.63 ≈ 1.587 hours, which rounds to 1.8 hours. Thus, the correct answer is Option C. Other options are incorrect as they either miscalculate the work rates or fail to consider the combined effort of the gardener and the sprinklers.
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