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tan and Hilda can mow the lawn in 60 min if they work together. If Hilda works twice as fast as Stan, how long does it take Stan to mow the lawn alone? Need Help? Read it Watch it

Ask by Donnelly Phillips. in the United States
Jan 27,2025

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Answer

Stan takes 180 minutes (3 hours) to mow the lawn alone.

Solution

Let's solve the problem step-by-step. **Given:** 1. **Together**, Stan and Hilda can mow the lawn in **60 minutes**. 2. **Hilda** works **twice as fast** as **Stan**. **Let's Define:** - Let \( S \) = the rate at which Stan can mow the lawn alone (lawns per minute). - Since Hilda is twice as fast, her rate \( H = 2S \). **Together, their combined rate is:** \[ S + H = S + 2S = 3S \] They can mow the lawn together in 60 minutes, so: \[ 3S \times 60 = 1 \text{ lawn} \] \[ 180S = 1 \] \[ S = \frac{1}{180} \text{ lawns per minute} \] **Time for Stan to mow alone:** \[ \text{Time} = \frac{1 \text{ lawn}}{S} = \frac{1}{\frac{1}{180}} = 180 \text{ minutes} \] **Conclusion:** Stan alone would take **180 minutes** (which is **3 hours**) to mow the lawn. **Answer:** Stan takes 180 minutes (three hours) to mow the lawn by himself.

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Let’s break it down! If Hilda works twice as fast as Stan, we can set Stan’s rate as \( r \) and Hilda’s rate as \( 2r \). Working together, their combined rate becomes \( r + 2r = 3r \). If they can mow the lawn together in 60 minutes, then: \[ 3r \cdot 60 = 1 \text{ (one lawn)} \] This simplifies to \( r = \frac{1}{180} \), meaning Stan mows \(\frac{1}{180}\) of the lawn in one minute. To find out how long it takes Stan to mow the lawn alone, we calculate: \[ \text{Time} = \frac{1}{\frac{1}{180}} = 180 \text{ minutes.} \] So, Stan takes 180 minutes to mow the lawn by himself! Now, if you think about it, while mowing the lawn can seem like a chore, it’s a great opportunity to enjoy some outdoor time. Whether you pop in your earbuds to listen to music or just soak in the sun, make the most of your lawn care sessions! And don’t forget to check out innovative lawn care gadgets that could make the task easier and more enjoyable, like self-propelled mowers or string trimmers!

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