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On a particular trip, Jane drove x miles at 30 miles per hour and y

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iamdp
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On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   Updated on: 10 Jun 2015, 07:11
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On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

(1) y > x + 60
(2) y/x > 4/3
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B

Originally posted by iamdp on 10 Jun 2015, 06:19.
Last edited by Bunuel on 10 Jun 2015, 07:11, edited 1 time in total.
Edited the question.
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On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   10 Jun 2015, 07:38
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dpo28 wrote:
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

(1) y > x + 60
(2) y/x > 4/3


On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

\(average \ speed = \frac{total \ distance}{total \ time}=\frac{x+y}{(\frac{x}{30}+\frac{y}{40})}=\frac{120(x+y)}{4x+3y}\)

Thus the question asks whether \(\frac{120(x+y)}{4x+3y}>35\).
After simplifying the question becomes: is \(\frac{y}{x}>\frac{4}{3}\).

(1) y > x + 60.

If x = 1 and y = 100, then y/x > 4/3.
If x = 1000 and y = 1200, then y/x < 4/3.

Not sufficient.

(2) y/x > 4/3. Directly gives an answer to our question. Sufficient.

Answer: B.

Hope it's clear.

Alternatively, notice that 35 miles per hour is halfway between 30 and 40 miles per hour. Now, for the average speed to be exactly 35 miles per hour, the amount of time spent to cover x miles (x/30 hours) must equal to the amount of time spent to cover y miles (y/40 hours). The average speed to be greater than 35 miles per hour, the amount of time spent to cover x miles at the slower speed (x/30 hours) must be less than the amount of time spent to cover y miles at the faster speed(y/40 hours):

x/30 < y/40.

Then continue as above.
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On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   10 Jun 2015, 07:37
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dpo28 wrote:
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

(1) y > x + 60
(2) y/x > 4/3



35 miles this is average speed if both distance will take equal time.
For example x = 300 miles on the speed 30 mph - 10 hours
and y = 400 on the speed 40 mph - 10 hours

So for have average speed more than 35 miles Jane should spend more time on distance y than on distance x
time = distance / speed

\(\frac{y}{40}>\frac{x}{30}\) --> \(\frac{y}{x}>\frac{4}{3}\)

1) this statement insufficient because we can't find ratio of distances x and y from given information

2) This statement gives us direct answer on the question.
Sufficient

Answer is B
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On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   11 Jun 2015, 00:03
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Hi Bunuel

i found another explanation for this question

it says that avg speed ie 4 is one away from 3 and 4 away from 8. Therefore time spent travelling at 3 m/hr is 4/5 of total.

I know this explanation is in compliance with the weighted average formula.

Can you plz elaborate on this method how it is 4/5 and not 1/5
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On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   Updated on: 11 Jun 2015, 04:12
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dpo28 wrote:
Hi Bunuel

i found another explanation for this question

it says that avg speed ie 4 is one away from 3 and 4 away from 8. Therefore time spent travelling at 3 m/hr is 4/5 of total.

I know this explanation is in compliance with the weighted average formula.

Can you plz elaborate on this method how it is 4/5 and not 1/5


Step 1: The distance between 3 and 8 is 5

Step 2: Realize that Weighted Average of 3 and 8 is 4

Step 3: Distance of 3 from Average 4 is 1 AND Distance of 8 from Average 4 is 4

Step 4: S1 / S2 = T2 / T1 by property because Speed S is Inversely proportional to Time T

Step 5: i.e. Speed 3 will take 4/5 of Total time and 8 will take 1/5 of Total time

I hope it clears!!!

Originally posted by GMATinsight on 11 Jun 2015, 03:51.
Last edited by GMATinsight on 11 Jun 2015, 04:12, edited 1 time in total.
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Re: On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   11 Jun 2015, 06:09
Seriously, how can you simplify so fast to this;
Quote:
Thus the question asks whether 120(x+y)/(4x+3y)>35.
After simplifying the question becomes: is y/x>4/3.
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Re: On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   11 Jun 2015, 06:14
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tjerkrintjema wrote:
Seriously, how can you simplify so fast to this;
Quote:
Thus the question asks whether 120(x+y)/(4x+3y)>35.
After simplifying the question becomes: is y/x>4/3.


120(x+y)/(4x+3y)>35

Since x and y are Positive Numbers hence you can cross multiply

120x + 120 y > 35*(4x+3y)

i.e. 120x + 120 y > 140x + 105y

i.e. 15y > 20x

i.e. 3y > 4x

i.e. (y/x) > (4/3)

I hope it clears your doubt!
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Re: On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   14 Sep 2015, 17:29
Harley1980 wrote:
dpo28 wrote:
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

(1) y > x + 60
(2) y/x > 4/3



35 miles this is average speed if both distance will take equal time.
For example x = 300 miles on the speed 30 mph - 10 hours
and y = 400 on the speed 40 mph - 10 hours

So for have average speed more than 35 miles Jane should spend more time on distance y than on distance x
time = distance / speed

\(\frac{y}{40}>\frac{x}{30}\) --> \(\frac{y}{x}>\frac{4}{3}\)

1) this statement insufficient because we can't find ratio of distances x and y from given information

2) This statement gives us direct answer on the question.
Sufficient

Answer is B



Harley1980
Could you please elaborate on how does one say that " average speed more than 35 miles Jane should spend more time on distance y than on distance x"
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On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   14 Sep 2015, 23:35
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earnit wrote:
Harley1980
Could you please elaborate on how does one say that " average speed more than 35 miles Jane should spend more time on distance y than on distance x"


Hello earnit

This is weighted average question
We can imagine scales:
on one side --------------------- on another side
speed 40 mph ----------------- 30mph

if both side have equal weight (in our case weight is time) when speed will be in middle:
speed 40 mph--------------------- 30mph
10 hours --------------------------10 hours

Average = 35 mph
===============================

if we shift our weight to left: more time with speed 40 mph then average will grow

speed 40 mph---------------------30mph
20 hours---------------------------0 hours

Average = 40 mph
===============================

if we shift our weight to right: more time with speed 30 mph then average will decline

speed 40 mph--------------------- 30mph
0 hours --------------------------- 20 hours

Average = 30 mph

So if we want average to be more than 35 mph we should put more weight on 40 mph scale (distance y in this question)

Try to read Karishma's articles on this topic. She like this topic and write really good posts about it.
At first weighted average was very difficult for me but when I read her articles and solve like 50 tasks this topic became very intuitive:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/12 ... -averages/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... ge-brutes/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/09 ... difficult/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/12 ... -question/

There is much more articles I just post first that I find. You can use search by words "weighted average"
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Re: On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   16 Mar 2017, 16:02
Bunuel,

If y=41miles and x=40 miles
the average speed will be 34,7 (less than 35!)

41 miles = ~1 hour
40 miles = ~1 hour and 20 minutes

total distance: 81 miles/ 2hours and 20 minutes = 37,7 miles.

Am I doing something wrong?



Bunuel wrote:
dpo28 wrote:
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

(1) y > x + 60
(2) y/x > 4/3


On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

\(average \ speed = \frac{total \ distance}{total \ time}=\frac{x+y}{(\frac{x}{30}+\frac{y}{40})}=\frac{120(x+y)}{4x+3y}\)

Thus the question asks whether \(\frac{120(x+y)}{4x+3y}>35\).
After simplifying the question becomes: is \(\frac{y}{x}>\frac{4}{3}\).

(1) y > x + 60.

If x = 1 and y = 100, then y/x > 4/3.
If x = 1000 and y = 1200, then y/x < 4/3.

Not sufficient.

(2) y/x > 4/3. Directly gives an answer to our question. Sufficient.

Answer: B.

Hope it's clear.

Alternatively, notice that 35 miles per hour is halfway between 30 and 40 miles per hour. Now, for the average speed to be exactly 35 miles per hour, the amount of time spent to cover x miles (x/30 hours) must equal to the amount of time spent to cover y miles (y/40 hours). The average speed to be greater than 35 miles per hour, the amount of time spent to cover x miles at the slower speed (x/30 hours) must be less than the amount of time spent to cover y miles at the faster speed(y/40 hours):

x/30 < y/40.

Then continue as above.
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Re: On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   17 Mar 2017, 02:20
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latinamerica2016 wrote:
Bunuel,

If y=41miles and x=40 miles
the average speed will be 34,7 (less than 35!)

41 miles = ~1 hour
40 miles = ~1 hour and 20 minutes

total distance: 81 miles/ 2hours and 20 minutes = 37,7 miles.

Am I doing something wrong?



Bunuel wrote:
dpo28 wrote:
On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

(1) y > x + 60
(2) y/x > 4/3


On a particular trip, Jane drove x miles at 30 miles per hour and y miles at 40 miles per hour. Was her average speed for the trip greater than 35 miles per hour?

\(average \ speed = \frac{total \ distance}{total \ time}=\frac{x+y}{(\frac{x}{30}+\frac{y}{40})}=\frac{120(x+y)}{4x+3y}\)

Thus the question asks whether \(\frac{120(x+y)}{4x+3y}>35\).
After simplifying the question becomes: is \(\frac{y}{x}>\frac{4}{3}\).

(1) y > x + 60.

If x = 1 and y = 100, then y/x > 4/3.
If x = 1000 and y = 1200, then y/x < 4/3.

Not sufficient.

(2) y/x > 4/3. Directly gives an answer to our question. Sufficient.

Answer: B.

Hope it's clear.

Alternatively, notice that 35 miles per hour is halfway between 30 and 40 miles per hour. Now, for the average speed to be exactly 35 miles per hour, the amount of time spent to cover x miles (x/30 hours) must equal to the amount of time spent to cover y miles (y/40 hours). The average speed to be greater than 35 miles per hour, the amount of time spent to cover x miles at the slower speed (x/30 hours) must be less than the amount of time spent to cover y miles at the faster speed(y/40 hours):

x/30 < y/40.

Then continue as above.


Are you talking about the second statement? If yes, then you cannot use y = 41 miles and x = 40 miles because these values do not satisfy the condition y/x > 4/3.
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Re: On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink] New post   12 Sep 2023, 09:29
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Re: On a particular trip, Jane drove x miles at 30 miles per hour and y [#permalink]
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