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

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Manifesting710
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Marcus performed a short test of his experimental race car by driving [#permalink] New post   18 Feb 2024, 06:47
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­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 ­
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C
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Re: Marcus performed a short test of his experimental race car by driving [#permalink] New post   18 Feb 2024, 07:37
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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 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
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Re: Marcus performed a short test of his experimental race car by driving [#permalink] New post   18 Feb 2024, 08:24
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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

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Re: Marcus performed a short test of his experimental race car by driving [#permalink] New post   17 Mar 2024, 09:28
gmatophobia how would you solve this with teeter totter?
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Marcus performed a short test of his experimental race car by driving [#permalink] New post   23 Mar 2024, 17:39
QuantMadeEasy 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 ­

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???­
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Re: Marcus performed a short test of his experimental race car by driving [#permalink] New post   24 Mar 2024, 02:08
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deeprest wrote:
QuantMadeEasy 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 ­

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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Targeting high GMAT Quant Score:
Udemy course: Best GMAT Math 5 Week Course | Target GMAT Focus 705+­

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

­
It should be \(90 = \frac{120}{1 + \frac{60}{x}}\) instead.

If you solve with the numbers given in the question, then it's \(90 = \frac{2}{\frac{1}{60} + \frac{1}{x}}\). Both of those give x = 180.­
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Re: Marcus performed a short test of his experimental race car by driving [#permalink] New post   24 Mar 2024, 07:39
Lets change the total miles from 1 mile per lap to 180 miles per lap (Using 180 because 90 and 60 are both go into 180).

Time for Lap 1: 180 miles at a speed of 60mph = 3 total hours
Time for Lap 2: 180 miles at an unknown speed = 'x' total hours

Average Speed = Total Distance/Total Time
90 mph = 360 (Lap 1: 180mles + Lap 2: 180miles)/3 + 'x' (x being the the total time it took to finish the second lap which we don't know yet)

Now you can use the answer choices but it's pretty easy to see that x has to equal 1 so that when 360 is divided by 4 we get 90.

If x equal's 1 that means it took Marcus 1 hour to complete the second lap of 180 miles and thus his speed must have been 180 miles per hour!

So C is our answer.
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Re: Marcus performed a short test of his experimental race car by driving [#permalink] New post   08 Apr 2024, 14:19
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quickest way for me or maybe I got lucky:
­1/60 + 1/x = 2/90
1/x = 1/45 - 1/60
realize common denominator is 180
1/x = (4-3)/180
1/x = 1/180
x = 180
 
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Re: Marcus performed a short test of his experimental race car by driving [#permalink]
08 Apr 2024, 14:19
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