Question

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 8 miles per hour. Sam walks at the rate of 9 miles per hour. Assume they start walking from the same place and walk in a straight line. Sam starts 34 hours after Leona. Answer the questions that follow. Hint: Distance = Rate × Time.

a. How many miles would each have walked?  (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Distance walked _____ miles

b. How long will it take Sam to meet Leona?  (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Time taken ____ hours

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 41 mph speed. The bus traveling west has a 36 mph speed. In how many hours will the buses be 616 miles apart?

Time taken_____ hours

Answer 1

Sam rate = 9 miles per hr

Leona rate = 8 miles per hr

Sam starts after 34 hours. Distance travelled by Leona in 34 hours = 34*8 = 272 miles

Difference in rate of Sam and Leona is 9-8 = 1 mile per hr.

Time taken to cover the distance of 272 miles will be = 272/1 = 272 hours

So, Sam will take 272 hours to meet Leona

Distance walked by both before they meet will be same

Distance travelled by Sam in 272 hours = Time*Rate = 272*9 = 2448 miles

a) 2448 miles

b) Time take is 272 hours

c) Since the two buses are travelling in opposite direction, the relative rate will be sum of the rate of two buses = 41 + 36 = 77 miles per hour

So, each hour, distance between the two will be 77 miles

Time to cover 616 miles = Distance/rate = 616/77 = 8 hours