On a recent trip, Mary drove 50 miles. What was the average

SOLUTION

On a recent trip, Mary drove 50 miles. What was the average speed at which she drove the 50 miles?

\(average \ speed=\frac{total \ distance}{total \ time}\) --> \(average \ speed=\frac{50}{total \ time}\). So, as we can see all we need to find is the total time spent on this trip.

(1) She drove 30 miles at an average speed of 60 miles per hour and then drove the remaining 20 miles at an average speed of 50 miles per hour. \(total \ time=\frac{30}{60}+\frac{20}{50}\). Sufficient.

(2) She drove a total of 54 minutes. Directly gives us the total time spent. Sufficient.

Answer: D.
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Hello Bunuel,

My initial thought was to choose D since I had the same solution process which you described.
But then I thought to myself that no where in the question or the statements was it mentioned that Mary drove at a constant rate.

I guess I got confused between the types of questions where I can use the total distance/ total time to get the average speed, and others where I have to compute each trip on its own to get the total average.

I'm not sure if you get my point on this? because I faced several problems where if I simply use total distance and total time, it would yield a wrong answer. Please help me to clarify this misunderstanding

Thanks

The question asks: what was the average speed at which she drove the 50 miles?

Now, the average speed equals to (total distance)/(total time) irrespective whether the distance was covered at a constant speed or not.
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I'm still confused about 2nd option.
Case A:-
Travelled 30 miles in 30 mints. Speed =dist/time = 30/0.5= 60 mph
Travelled 20 miles in 24 mints. Speed = dist/time = 20/(2/5) = 50mph
Avg = 55mph

Case b:-
Travelled 30 miles in 20 mints. Speed = dist/time= 30/(1/3) = 90mph
Travelled 20 miles in 34mints. Speed = dist/time = 20/(34/60) = 35.3mph
Avg = (90+35.3)/2= 62.64mph

Now in both cases we are getting different avg speed. Please comment

You are using info from (1) for (2).

In fact the second statement is very easy. We know that Mary drove 50 miles, and we need to find the average speed at which she drove those 50 miles. (2) says that she drove a total of 54 minutes (0.9 hours), thus \(average \ speed=\frac{total \ distance}{total \ time}=\frac{50}{0.9}\). Sufficient.

Hope it helps.
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We are being tested on average speed. The formula for average speed is:

average speed = total distance/total time

We are given that the total distance is 50 miles, so we can substitute 50 miles into our formula.

average speed = 50/total time

Thus, if we can determine the total time, we can determine the average speed.

Statement One Alone:

She drove 30 miles at an average speed of 60 miles per hour and then drove the remaining 20 miles at an average speed of 50 miles per hour.

We are given that Mary first drove 30 miles at an average speed of 60 mph.

Since time = distance/rate, we can say:

time for the first 30 miles = 30/60 = ½ hour

We are also given that Mary drove the remaining 20 miles at an average speed of 50 miles per hour. Thus, we can say:

time for the remaining 20 miles = 20/50 = 2/5 hours

So we know that total time = ½ + 2/5 = 5/10 + 4/10 = 9/10 hours. Since we have the total time, we can determine average speed. Statement one is sufficient to answer question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

She drove a total of 54 minutes.

We are given the total time, so statement two is also sufficient to answer the question.

The answer is D.
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Hi!

How do you know that this is a 650 level question?

Difficulty level (seen in tags) is calculated automatically based on the timer stats from the users which attempted the question. The difficulty level of this question is thus sub-600. As you can see 77% of the users attempting the question answered it correctly spending at average 01:39 minutes.
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On a recent trip, Mary drove 50 miles. What was the average speed at which she drove the 50 miles?

\(Speed = \frac{Distance}{Time}\)

\(Avg. Speed = \frac{Total Distance}{Total Time}\)

As the question is asking for Average Speed and we are already aware of distance, which means if we get some information on - how much time Mary drove we will be able to calculate the average speed.

Note, only knowing time would be sufficient for us to determine if the sentence is sufficient or not. We need calculate the exact average speed as this is DS question.

(1) She drove 30 miles at an average speed of 60 miles per hour and then drove the remaining 20 miles at an average speed of 50 miles per hour.

As we are given two different speeds for two split of distances, we should be able to calculate the time taken for these two speeds which will be our total time taken.

As we will be able to calculate time, this statement should be sufficient.

Hence, (1) =====> is SUFFICIENT

(2) She drove a total of 54 minutes.

This directly gives us the total time taken.

Once again, this statement should be sufficient.

Hence, (2) =====> is SUFFICIENT

Hence, Answer is D
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Target question: What was Mary's average speed for the 50-mile trip?
Average speed = (total distance)/(total travel time)
= (50 miles)/(total travel time)

As you can see, we need only determine the total travel time in order to answer the target question.

Statement 1: She drove 30 miles at an average speed of 60 miles per hour and then drove the remaining 20 miles at an average speed of 50 miles per hour.
For both parts of her journey, we COULD determine the travel time, so we COULD find the total travel time, which means we COULD calculate Mary's average speed
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: She drove a total of 54 minutes.
Perfect! Her total travel time is 54 minutes, so we COULD calculate Mary's average speed
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Bunuel EducationAisle can we use Allegation for (1) and get our answer?

Hoozan Sorry, I am not Bunuel, but I would love to help you out-

Yes, you can get to the answer via "Allegation".
You will get the equation-

\(\frac{50-x}{x-60} = \frac{3}{2}\)

Upon solving you will \(x = 56 m/hr\)
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