The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes

It takes 15 minutes longer to walk, so 30 = 4.5 + x + 15

x=10.5 minutes

Answer: A
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Using the Formula
t= d/v where t=time taken , d= distance , v = avg speed
We get t for walk is = 1.5/3=15/30=1/2 hour = 30 minutes
we get t for train journey = 1.5/20=15/200=3/40 hours = (3/40)*60 = 9/2 minutes = 4.5 minutes
since x minutes is taken additionally for train commute we must add x to 4.5 to get x+4.5 minutes. Still this is 15 minutes less than time taken by walking.
So,
x+4.5+15 = 30
=> x = 10.5

Answer (A)

Hope this helps
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In such long stem questions, analyse each sentence as you go.

"Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour," - When she walks, she takes 1/2 hr or 30 mins to reach work.


"or she can ride the train to work at a constant rate of 20 miles per hour." - When she takes the train, she takes (1.5/20)*60 mins = 4.5 mins to reach work.


"If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work." - Time taken to reach work by train = 4.5 + x

"If it takes Darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train," - it takes her 30 mins to walk so it takes her 15 mins to go by train.

"what is the value of x? "
15 = 4.5 + x
x = 10.5
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Ok, for this one I know that we have nice algebraic solutions. Try eliminating answer choices.
Speed when walking = 3 miles per hour => to travel 1.5 we need 30 minutes of walking. Total time taken by train = 15 minutes . This includes train journey time and walking and waiting time (x). Now x must be less than 15.
The only answer that fits the bill is A i.e. 10.5.

Why are we assuming that the distance between Darcy's home to work(which is 1.5 miles) is the same distance between the two stations?

If you're answer is any of the following :

- There is no other information given so, we should assume.
-We need an answer and hence this is the only way to get as we would not get an answer if we bring in other distance variable.
-you've got to work with what you have.
-Assuming like this is correct and this is very much a GMAT like question.

Then, I'm scared, very very scared!! a person like me who is moving at Q45-47 is very very scared!! Help

Actual GMAT questions will usually not require you to make assumptions. That said, there are experimental questions in the actual test too and if you are unable to solve a PS question without making an assumption, make it and move on.
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I did this problem in roughly the same way as ajdse22 above.

I suspect I got a little lucky (just two quick calculations in my head and no algebra with respect to train's rate and X minutes).

While reading the question, I calculated in my head that it took her half an hour or 30 minutes to walk to work.

The last sentence says "15 more minutes" to walk than time taken for "train-plus-extra [that they're calling X minutes]." Or, walk time - 15 gives us the time for train-plus-extra. (30 - 15) means she has only 15 minutes for that train-plus-extra route.

A quick glance at answers; B, 15, caught my eye. If the extra, X minutes, were 15 minutes, 15 (what she has) - 15 (answer choice) = 0. There would be no time for the train. Answer has to be less than 15. There's one choice: A.
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We are given that the distance to work is 1.5 miles. Thus, the time it takes Darcy to walk to work is 1.5/3 = 15/30 = 1/2 hour, or 30 minutes.

When she takes the train, her time is x + 1.5/20 = x + 15/200 = x + 3/40 hours. Let’s convert 3/40 hours to minutes:

3/40 hours = 3/40 x 60 = 4.5 minutes

Since she spends 15 more minutes walking than she does taking the train:

4.5 + x + 15 = 30

x = 10.5 minutes

Answer: A
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misunderstood and as the result overcomplicated the question
I was under impression that this 1.5 miles commute includes train and walking as well ) so that:
1.5/20 + 1.5-x/ 3= 0.25h

sometimes I really trick myself more than the question does

it seems to me that the equation ought to look like this:
1.5/3-[(1.5-3x/60)/20]+x/60=1/4
can someone point out my error?
thank you.

plz read my comment above
she travels 1,5 entirely by taking train

so it's more like:
1.5/20 + x minutes for walking to/from the train station= 15 minutes
4.5 minutes + x minutes = 10.5 minutes