The distance on a bike path between Westfield and Southborough is 46 mi. Tracey leaves Westfield heading to Southborough cycling at a constant rate of 15 mph. Emma leaves her house at the same time and cycles along the same path from Southborough to meet Tracey. Her cycling rate is 8 mph. How many hours will it take until the two friends meet along the bike path?

Question

Annika

Mathematics

28 December, 08:52

The distance on a bike path between Westfield and Southborough is 46 mi. Tracey leaves Westfield heading to Southborough cycling at a constant rate of 15 mph. Emma leaves her house at the same time and cycles along the same path from Southborough to meet Tracey. Her cycling rate is 8 mph. How many hours will it take until the two friends meet along the bike path?

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Nikhil Bauer · Answer 1

Answer: 2 hr.

Explanation: Think back to rate of change. d = rt, r = d/t, t = d/r. In this case, we will be using d = rt. Mph would be r, rate, so you would categorize 15 mph and 8 mph under rate. t should represent the time each cyclist traveled. Tracey's and Emma's distance, d, would be the same as their mph, hence Tracey's being 15t and Emma's would be 8t. When you add Tracey's distance plus Emma's distance, you end up with 46 mi. Now, you need to combine like terms, which should look like 15t + 8t = 46. Add 15 and 8 to get 23, so it should be 23t = 46 now. Then, divide both sides of the equation by 23 and now you should have your answer, t = 2 hr.