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

Question

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

A. 120
B. 150
C. 180
D. 210
E. 240

MartyMurray · Accepted Answer

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

Total Distance: 2 miles

Average Rate:  90 miles per hour

Total Time: Distance/Rate = 2/90 hour

Time First Mile: 1/60 hour

Time Second Mile: 2/90 - 1/60 = 4/180 - 3/180 = 1/180 hour

Rate Second Mile: 180 miles per hour

A. 120
B. 150
C. 180
D. 210
E. 240

Correct answer:  C

gmatophobia · Answer

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{	ext{Distance}}{	ext{Time}}

Speed for the second mile =  \frac{1}{\frac{1}{180}} = 180  mph

Option C

QuantMadeEasy · Answer

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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Dmytr0 · Answer

gmatophobia  how would you solve this with teeter totter?

deeprest · Answer

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

Bunuel · Answer

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.

Jake7Wimmer · Answer

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.

jayouh · Answer

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

OmerKor · Answer

Hi  gmatophobia ,

​​​​​​​I didn't understand your second approach.
I solved the problem in a different way but still I want to strengthen my toolkit for solving this kind of problems. 
Could you please elaborate the algebra you did?
Specifically: how did you get there?   Total time taken in minutes to cover two miles = 290∗60=43

GMATinsight · Answer

Average Speed = 60 miles per hour (i.e. 60 miles in 60 minutes i.e. 1 miles every minute)

i.e. Time to travel the first mile = 1 mins

Total distance travelled = 2 miles
Average speed = 90 miles / hour (i.e. 90 miles in 60 minutes i.e. 1.5 miles in 1 minute)

Time to travel 2 miles at this speed = 2/1.5 = 4/3 minute = 1 minutes and 20 seconds

i.e. Second mile was travelled in 20 seconds
i.e. speed was 3 miles in a minute 
i.e. 180 miles in 60 minutes (miles/Hour)
Speed = 180 m/h

Answer: Option C

A_Nishith · Answer

Total time taken in minutes to cover two miles = (2/90)∗60=4/3 min.

Time taken (in minutes) to cover the first mile = 1 minute

Time taken (in minutes) to cover the second mile = 4/3−1=1/3 min 
Time taken (in hours) to cover the second mile = (1/3)∗1/60=1/180 hours

Speed for the second mile =Distance/Time
Speed for the second mile =1mile / (1/180)hrs = 180 mph

Option C

Danou · Answer

I am not sure I understand the path to the answer at all. Appreciate any help!
I have been trying to use this formula:
 
Distance = speed x time

Having no success in coming close to the answer...
Any help is much appreciated!

glagad · Answer

Hi,

Is there a way to solve this question using the alligation method? Would appreciate responses there.

Dream009 · Answer

Avg speed of overall journey = 2s1*s2/s1+s2
90 = 2*60s2/s1+s2
3/4 = s2/ 60+s2
3/4*60 + 3/4 s2 = s2
3/4*60 = 1/4 s2
=> s2 = 180

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

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