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from station A to station C

by Needgmat » Wed Sep 28, 2016 9:42 am

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A train traveled from station A to station B at an average speed of 80 kilometers per hour and then from station B to station C at average speed of 60 kilometers per hour. If the train did not stop at station B, what was the average speed at which the train traveled from station A to station C?

1) The distance that the train traveled from station A to station B was 4 times the distance that the train traveled from station B to station C.

2) The amount of time that it took the train to travel from station A to station B was 3 times the amount of time that it look the train to travel from station B to station C.



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by MartyMurray » Thu Sep 29, 2016 6:26 am

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First, here is what Average Speed is not. Except in certain rare cases, Average Speed is not equal to (Speed 1 + Speed 2)/2.

The 100% of the time accurate way to calculate average speed is Total Distance/Total Time = Average Speed.

Now let's look at this question.

Question: A train traveled from station A to station B at an average speed of 80 kilometers per hour and then from station B to station C at average speed of 60 kilometers per hour. If the train did not stop at station B, what was the average speed at which the train traveled from station A to station C?

We don't know total time or total distance. We don't know relative distances of the two parts of the trip either. For all we know the distance from A to B is 1000 times the distance from B to C.

So the average speed could be closer to 80 kilometers per hour or to 60 kilometers per hour or could be right in the middle at 70 kilometers per hour.

Let's see whether the statements help.

Statement 1: The distance that the train traveled from station A to station B was 4 times the distance that the train traveled from station B to station C.

This does not give us the time spent traveling, but given that we have the speeds for both parts of the trip and the relative distances of the two parts, it makes sense that we would be able to calculate the average speed for the entire trip.

Here's one way.

Total Distance = 4x + x = 5x

Total Time = 4x/80 + x/60

Average Speed = Total Distance/Total Time = 5x/(4x/80 + x/60) = 5x/(16x/240)

The x's cancel out.

5x/(16x/240) = 5/(16/240) = 5 * 240/16 = 75.

So 75 is the average speed.

Sufficient.

Statement 2: The amount of time that it took the train to travel from station A to station B was 3 times the amount of time that it look the train to travel from station B to station C.

It makes sense that this would be sufficient because if we have the speeds, from the question, and the relative times, from this statement, we can calculate the relative distances, which information is what we got from Statement 1.

Distance A to B: 80 * 3T = 240T

Distance B to C: 60 * T = 60T

Distance A to B/Distance B to C = 4

Now we have Statement 1 again.

Sufficient.

The correct answer is D.

Alternate Method

Statement 1: The distance that the train traveled from station A to station B was 4 times the distance that the train traveled from station B to station C.

Plug in numbers that fit.

Distance A to B: 240

Distance B to C: 60

Time A to B: 3

Time B to C: 1

Total Distance/Total Time = 300/4 = 75

Try another set of numbers.

Distance A to B: 80

Distance B to C: 20

Time A to B: 1

Time B to C: 1/3

Total Distance/Total Time = 100/(4/3) = 75

Same result.

Sufficient.

Statement 2 also can be proved sufficient using plugged in numbers.

The correct answer is D.
Last edited by MartyMurray on Thu Sep 29, 2016 8:14 am, edited 2 times in total.
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by GMATGuruNY » Thu Sep 29, 2016 6:33 am

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Needgmat wrote:A train traveled from station A to station B at an average speed of 80 kilometers per hour and then from station B to station C at average speed of 60 kilometers per hour. If the train did not stop at station B, what was the average speed at which the train traveled from station A to station C?

1) The distance that the train traveled from station A to station B was 4 times the distance that the train traveled from station B to station C.

2) The amount of time that it took the train to travel from station A to station B was 3 times the amount of time that it look the train to travel from station B to station C.
Statement 2: The amount of time that it took the train to travel from Station A to Station B was 3 times that amount of time that it took the train to travel from Station B to Station C.
Thus, of every 4 hours traveled, 3 hours are traveled at 80 miles per hour and 1 hour is traveled at 60 miles per hour, implying that the average speed every 4 hours = (3*80 + 1*60)/4 = 300/4 = 75 miles per hour.
SUFFICIENT.

Statement 1: The distance that the train traveled from Station A to Station B was 4 times the distance that the train traveled from Station B to Station C.
Learn from Statement 2:
3 hours from A to B at 80 miles per hour = 240 miles.
1 hour from B to C at 60 miles per hour = 60 miles.
When the train travels for the times given in statement 2, the distance from A to B is 4 times the distance from B to C.
Implication:
The two statements convey the SAME INFORMATION.
Thus, since statement 2 is sufficient, statement 1 must also be SUFFICIENT.

The correct answer is D.
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by alanforde800Maximus » Wed May 16, 2018 2:50 am

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Marty Murray wrote:First, here is what Average Speed is not. Except in certain rare cases, Average Speed is not equal to (Speed 1 + Speed 2)/2.

The 100% of the time accurate way to calculate average speed is Total Distance/Total Time = Average Speed.

Now let's look at this question.

Question: A train traveled from station A to station B at an average speed of 80 kilometers per hour and then from station B to station C at average speed of 60 kilometers per hour. If the train did not stop at station B, what was the average speed at which the train traveled from station A to station C?

We don't know total time or total distance. We don't know relative distances of the two parts of the trip either. For all we know the distance from A to B is 1000 times the distance from B to C.

So the average speed could be closer to 80 kilometers per hour or to 60 kilometers per hour or could be right in the middle at 70 kilometers per hour.

Let's see whether the statements help.

Statement 1: The distance that the train traveled from station A to station B was 4 times the distance that the train traveled from station B to station C.

This does not give us the time spent traveling, but given that we have the speeds for both parts of the trip and the relative distances of the two parts, it makes sense that we would be able to calculate the average speed for the entire trip.

Here's one way.

Total Distance = 4x + x = 5x

Total Time = 4x/80 + x/60

Average Speed = Total Distance/Total Time = 5x/(4x/80 + x/60) = 5x/(16x/240)

The x's cancel out.

5x/(16x/240) = 5/(16/240) = 5 * 240/16 = 75.

So 75 is the average speed.

Sufficient.

Statement 2: The amount of time that it took the train to travel from station A to station B was 3 times the amount of time that it look the train to travel from station B to station C.

It makes sense that this would be sufficient because if we have the speeds, from the question, and the relative times, from this statement, we can calculate the relative distances, which information is what we got from Statement 1.

Distance A to B: 80 * 3T = 240T

Distance B to C: 60 * T = 60T

Distance A to B/Distance B to C = 4

Now we have Statement 1 again.

Sufficient.

The correct answer is D.

Alternate Method

Statement 1: The distance that the train traveled from station A to station B was 4 times the distance that the train traveled from station B to station C.

Plug in numbers that fit.

Distance A to B: 240

Distance B to C: 60

Time A to B: 3

Time B to C: 1

Total Distance/Total Time = 300/4 = 75

Try another set of numbers.

Distance A to B: 80

Distance B to C: 20

Time A to B: 1

Time B to C: 1/3

Total Distance/Total Time = 100/(4/3) = 75

Same result.

Sufficient.

Statement 2 also can be proved sufficient using plugged in numbers.

The correct answer is D.
Thanks for sharing number plugging approach that was helpful.
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