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if Henry can mow a certain lawn in 2 hrs2\,\text{hrs} and Nathan can mow it in 2.5 hrs2.5\,\text{hrs}, how long would it take them to mow it together with two lawnmowers

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Q. if Henry can mow a certain lawn in 2 hrs2\,\text{hrs} and Nathan can mow it in 2.5 hrs2.5\,\text{hrs}, how long would it take them to mow it together with two lawnmowers
  1. Calculate Henry's Rate: Calculate Henry's mowing rate per hour.\newlineHenry's rate = 1 lawn2 hours=0.5 lawn/hour.\frac{1 \text{ lawn}}{2 \text{ hours}} = 0.5 \text{ lawn/hour}.
  2. Calculate Nathan's Rate: Calculate Nathan's mowing rate per hour. Nathan's rate = 1 lawn2.5 hours=0.4 lawn/hour.\frac{1 \text{ lawn}}{2.5 \text{ hours}} = 0.4 \text{ lawn/hour}.
  3. Add Rates for Combined Rate: Add their rates together to find their combined rate.\newlineCombined rate = Henry's rate + Nathan's rate = 0.5lawnhour+0.4lawnhour=0.9lawnhour0.5 \frac{\text{lawn}}{\text{hour}} + 0.4 \frac{\text{lawn}}{\text{hour}} = 0.9 \frac{\text{lawn}}{\text{hour}}.
  4. Calculate Time for Mowing: Calculate the time it takes for them to mow the lawn together.\newlineTime = 1 lawnCombined rate=1 lawn0.9 lawn/hour=1.111…\frac{1 \text{ lawn}}{\text{Combined rate}} = \frac{1 \text{ lawn}}{0.9 \text{ lawn/hour}} = 1.111\ldots hours.

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