Myron Corporation Walking Race Math Problem

Leona and Sam Walking Race Problem

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?

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).