Myron Corporation Walking Race Math Problem

Leona and Sam Walking Race Problem

Myron Corporation is sponsoring a walking race at its company outing. Leona Jackson and Sam Peterson love to walk. Leona walks at the rate of 5 miles per hour. Sam walks at the rate of 6 miles per hour. Assume they start walking from the same place and walk in a straight line. Sam starts 1/2 hour after Leona. Answer the questions that follow. Hint: Distance = Rate × Time.

a. How long will it take Sam to meet Leona?

b. How many miles would each have walked?

c. Assume Leona and Sam meet in Lonetown Station where two buses leave along parallel routes in opposite directions. The bus traveling east has a 60 mph speed. The bus traveling west has a 40 mph speed. In how many hours will the buses be 600 miles apart?

Final Answer: Sam will take 2.5 hours to meet Leona, and they will both have walked 15 miles by then. The two buses departing from Lonetown Station will be 600 miles apart after 6 hours. Explanation:

For question a, since Leona walks at a rate of 5 miles per hour and Sam starts walking half an hour after her, Leona will have walked 2.5 miles (5 miles/hour × 0.5 hours) by the time Sam starts walking. Since Sam walks faster at a rate of 6 miles per hour, he is effectively closing the gap between them at a rate of 1 mile per hour (6 miles per hour - 5 miles per hour). Therefore, it will take Sam 2.5 hours (2.5 miles ÷ 1 mile/hour) to meet Leona.

For question b, Sam has walked for 2.5 hours at a rate of 6 miles per hour, so he has walked 15 miles (6 miles/hour × 2.5 hours). By the time they meet, Leona has been walking for 3 hours (her initial 0.5 hour head start + the 2.5 hours Sam was walking). At her rate of 5 miles per hour, she has also walked 15 miles (5 miles/hour × 3 hours).

For question c, the two buses are moving away from each other at a combined rate of 100 mph (60 mph for the one traveling east + 40 mph for the one traveling west). Therefore, they will be 600 miles apart after 6 hours (600 miles ÷ 100 miles/hour).

Question: What is the final answer to the walking race problem involving Leona and Sam? Explain the solution for each part of the question. Answer: Sam will take 2.5 hours to meet Leona, and they will both have walked 15 miles by then. The two buses departing from Lonetown Station will be 600 miles apart after 6 hours.
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