Marcus performed a short test of his experimental race car by driving

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 ­

To make calculation simple, let the two equal distance be 60miles each
First 60 miles covered with speed of 60miles per hours, therefore time taken is 1 hour
Let next 60 miles covered with speed of x miles per hours, therefore time taken is x/60 hours

Hence, total distance covered is 120 miles
Total time taken is (1 + x/60) hours

Average speed = total distance covered / total time taken
90 = 120 / (1 + x/60)
Solving for x = 180 miles per hour

IMO C
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­Coming back to this. Solving for x doesn't give 180???­

Approach 1: Using Formula

­When 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 speed

Total 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

­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 ­