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At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?

Notice that we are not told that the train travels at a constant speed.

(1) The trip was 460 miles long and took 4 hours to complete --> the average speed of the train was 460/4=115 miles per hour, but we don't know what was the speed of the train when it had completed half of the total distance (230 miles). Not sufficient.

(2) The train traveled at an average rate of 115 miles per hour on the trip. The same as above. Not sufficient.

(1)+(2) We only know that the average speed of the train was 115 miles per hour, which is not enough to determine the speed of the train when it had completed half of the total distance (230 miles). Not sufficient.

Re: At what speed was a train traveling on a trip when it had [#permalink]

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01 Aug 2013, 10:29

1

This post received KUDOS

At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?

(1) The trip was 460 miles long and took 4 hours to complete. The train could have been moving at a slower speed for the first part of the trip then faster for the second part to complete the journey in 4 hours. INSUFFICIENT

(2) The train traveled at an average rate of 115 miles per hour on the trip. We know nothing about distance and it's possible that the train was traveling at a slower rate for the first part of the trip then faster for the second part of the trip to average out to 115 MPH. INSUFFICIENT

1+2) There still is not enough information to solve for this problem. We know that the train averaged 115MPH and that it took four hours to complete the trip (i.e. it took 4 hours) but the train could have moved slower for the first portion of the trip and faster for the second portion of the trip. there is no way of knowing for sure. INSUFFICIENT

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28 Apr 2016, 13:52

As we don't know whether the train is travelling at a constant speed,the answer is got to be E Anyway for understanding here is a explaination Statement 1 gives information about the total distance traveled in total time which will give us the average speed, but we can't deduce anything about the speed of the train when it had completed half of its distance, So insufficient

Statement 2 gives information about the average speed, but we can't deduce anything about the speed of the train when it had completed half of its distance, So insufficient Combining both statements they are providing the same information We only know that the average speed of the train was 115 miles per hour, which is not enough to determine the speed of the train when it had completed half of the total distance (230 miles) So insufficient Correct Answer - E

At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?

(1) The trip was 460 miles long and took 4 hours to complete. (2) The train traveled at an average rate of 115 miles per hour on the trip.

Solution:

We need to determine at what speed a train was traveling when it completed ½ of its trip.

Statement One Alone:

The trip was 460 miles long and took 4 hours to complete.

With the information in statement one, we can determine the average speed of the train for the entire trip.

average speed = total distance/total time

average speed = 460/4

average speed = 115

Although we know that the train traveled at an average speed of 115 mph, we do not know whether the train traveled at a constant rate. Thus, we cannot determine the speed of the train when it completed half of the total distance. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The train traveled at an average rate of 115 miles per hour on the trip.

We see that statement two provides the same information as statement one and thus is also not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Since statements one and two provide identical information and are each insufficient, we know that the statements together are also insufficient.

The answer is E.
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

At what speed was a train traveling on a trip when it had [#permalink]

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23 Sep 2016, 12:49

If you recall your physics class in high school you can solve this question in less than 30 seconds...

For starters: The question asks for the instantaneous speed of the train.

In this world there are ONLY two WAYs in order to be able to know the instantaneous speed of any object.

1) If someone tells you the speed @ that specific instance (lol)

2) If you have a speed equation with the unknown variable being the time, i.e. s(t) = function of speed ... For example if we were in a position to derive from the given info an equation with 1 unknown like fore example..

Speed = 2t + 3 OR Speed = a*t^2 + t + t/2 + c/g ETC ... OR any type of equation with a single variable t for time

then the only thing you need to do is replace the variable t with the time instance asked in the question and you are done. Although be very careful with the units of t.

This question doesn't do any of the two so you should be able to pick E very quickly.

Some might argue that the constant rate might cause a problem but hey this is nothing more than an equation with 0 unknown or in other words it will have the form y=b. Since we talk for speed and time for convenience Speed = α where α can be any value.

So if the question was saying that for a journey of Gazillion hours the speed of the train was constant at a m/s then you know that s = a which means that throughout the whole journey its speed was CONSTANT and never changed.

At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?

(1) The trip was 460 miles long and took 4 hours to complete. (2) The train traveled at an average rate of 115 miles per hour on the trip.

Target question:At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?

Statement 1: The trip was 460 miles long and took 4 hours to complete. IMPORTANT: there is nothing in this question to suggest that the train is traveling at a CONSTANT speed. So, there's no way to determine the train's speed when it had competed half of the trip. To see what I mean, consider these two conflicting cases: Case a: the train travels the first half (230 miles) of the trip at a constant speed 230 mph (for 1 hour), and then travels the second half (230 miles) at a constant speed 230/3 mph (for 3 hours). In this case, the train was traveling at 230 mph when it had completed half of the total distance of the trip Case b: the train travels at a constant speed of 115 mph for the ENTIRE trip. In this case, the train was traveling at 115 mph when it had completed half of the total distance of the trip Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The train traveled at an average rate of 115 miles per hour on the trip. NOTE: This statement doesn't provide any new information. That is, from statement 1, we can already determine that the trains average speed = (460 miles)/(4 hours) = 115 mph. So, it's POSSIBLE to use the same counter-examples that we used for statement 1: Case a: the train travels the first half (230 miles) of the trip at a constant speed 230 mph (for 1 hour), and then travels the second half (230 miles) at a constant speed 230/3 mph (for 3 hours). In this case, the train was traveling at 230 mph when it had completed half of the total distance of the trip Case b: the train travels at a constant speed of 115 mph for the ENTIRE trip. In this case, the train was traveling at 115 mph when it had completed half of the total distance of the trip Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED, which means the combined statements are still NOT SUFFICIENT

We're asked to find that speed that a train traveling on a trip when it had completed half of the total distance of the trip.

1) The trip was 460 miles long and took 4 hours to complete.

Fact 1 gives us the information to find the AVERAGE speed of the train for the entire trip: 460/4 = 115 miles/hour

However, this is NOT what the question asks for. It's possible that the train changed speeds during the trip, so we don't know whether the train was actually going 115 miles/hour at the half-way point or not. Fact 1 is INSUFFICIENT

2) The train traveled at an average rate of 115 miles per hour on the trip.

Fact 2 gives us the same information that we determined in Fact 1 - and we still have the same issue as before (we don't know how fast the train was actually going at the half-way point). Fact 2 is INSUFFICIENT

Combined, we really have just one piece of information: the average speed for the entire trip - and we already know that that is not enough to answer the given question. Combined, INSUFFICIENT.