Manifesting710 wrote:
Marcus performed a short test of his experimental race car by driving 2 miles at a racetrack. To make some slow-speed observations of the performance of his race car, Marcus drove the first mile in 1 minute and averaged 60 mph (miles per hour). Marcus drove the second mile in less time than he drove the first mile and he averaged 90 mph for the entire 2-mile test drive. What was Marcus's average speed, in miles per hour, for the second mile?
A 120
B 150
C 180
D 210
E 240
Approach 1: Using FormulaWhen the distance covered is same, the overall average speed (\(S\)) is given by
\(S = \frac{2 * S_1 * S_2}{S_1+S_2}\)
\(S_1\) and \(S_2\) → Average Speed of Individual Segments
Here \(S = 90\); \(S_1 = 60\)
\(90 = \frac{2 * 60 * S_2}{60 + S_2}\)
\(3 = \frac{2 * 2 * S_2}{60 + S_2}\)
\(180 + 3S_2 = 4S_2\)
\(S_2 = 180 \) mph
Approach 2: Using the concept of average speedTotal time taken in minutes to cover two miles = \(\frac{2}{90 * 60} = \frac{4}{3}\)
Time taken (in minutes) to cover the second mile = \(\frac{4}{3} - 1= \frac{1}{3}\)
Time taken (in hours) to cover the second mile = \(\frac{4}{3} - 1= \frac{1}{3} * \frac{1}{60} = \frac{1}{180}\)
Speed for the second mile =\( \frac{\text{Distance}}{\text{Time}}\)
Speed for the second mile =\( \frac{1}{\frac{1}{180}} = 180\) mph
Option C