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A highway connects city A and city B and extends 2493 miles. Paul Simon begins in city A and drives at an average rate of 44 mph on the highway toward city B. At the same time John Smith begins in city B and drives on the highway at an average rate of 51 mph toward city A. If Paul and John maintain these average speeds, how long after they start will they meet? hr (Round to the nearest hundredth as needed.)

Ask by Rose Bolton. in the United States
Feb 04,2025

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Tutor-Verified Answer

Answer

They will meet after approximately 26.24 hours.

Solution

To determine how long it will take for Paul and John to meet, we can use the concept of relative speed. Here's the step-by-step solution: 1. **Combined Speed:** - Paul’s speed: 44 mph - John’s speed: 51 mph - Combined speed when moving towards each other: \(44 + 51 = 95\) mph 2. **Total Distance:** - The distance between city A and city B is 2493 miles. 3. **Time to Meet:** \[ \text{Time} = \frac{\text{Total Distance}}{\text{Combined Speed}} = \frac{2493 \text{ miles}}{95 \text{ mph}} \approx 26.2421 \text{ hours} \] 4. **Rounding:** - Rounding to the nearest hundredth: **26.24 hours** **Answer:** 26.24 hr

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Beyond the Answer

To find out how long it takes for Paul and John to meet, we can set up an equation based on their speeds and the total distance. Together, they are closing the distance between them at a combined speed of 44 mph + 51 mph = 95 mph. The total distance between them is 2493 miles. Now, we can calculate the time it takes to meet by using the formula: Time = Distance / Speed Time = 2493 miles / 95 mph ≈ 26.19 hours. So, Paul and John will meet approximately 26.19 hours after they start driving. Now, let’s give you some extra fun facts! Did you know that the world's longest road is the Pan-American Highway, stretching over 19,000 miles from Prudhoe Bay in Alaska to Ushuaia in Argentina? It would take you a long time to drive that highway, even at speeds over 50 mph! And speaking of highways, remember the importance of planning your route! While it's thrilling to hit the open road, don't forget to check for rest stops, food, and gas stations along the way. A well-planned road trip makes for a memorable journey!

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