Q:

Given the speeds of each runner below, determine who runs the fastest. Stephanie runs 10 feet per second. Stephanie runs 10 feet per second. Liz runs 420 feet in 46 seconds. Liz runs 420 feet in 46 seconds. Adam runs 1 mile in 427 seconds. Adam runs 1 mile in 427 seconds. Emily runs 667 feet in 1 minute. Emily runs 667 feet in 1 minute. Stephanie Stephanie Liz Liz Adam Adam Emily Emily Submit Answer

Accepted Solution

A:
9514 1404 393Answer:   AdamStep-by-step explanation:It is pretty easy to make comparisons to 10 ft/s.If Liz ran 10 ft/s, she would run 460 ft in 46 s. Since she runs 420 ft, she runs slower than that.If Emily ran 10 ft/s, she would run 600 ft in 1 minute, so Emily runs faster than that.If Adam ran 10 ft/s, he would only run 4270 ft in 427 seconds. Since he runs 5280 ft in that time, his speed is definitely greater than 10 ft/s.__At this point, we know that Adam and Emily run faster than Liz and Stephanie. So we need to compare Adam and Emily's rates. Adam's time for 1 mile is about 7 minutes. If Emily ran for 7 minutes, her distance would be less than 7×700 ft = 4900 ft, substantially less than 1 mile (5280 ft).Adam runs the fastest._____Comment on straightforward solutionEach rate can be computed by dividing distance by time:   Liz: (420 ft)/(46 s) = 9.13 ft/s   Adam: (5280 ft)/(427 s) = 12.37 ft/s   Emily: (667 ft)/60 s) = 11.12 ft/sAdam's is the highest, well above Stephanie's 10 ft/s.These calculations require a calculator. The solution above was done without a calculator.