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# A vehicle averaged x miles per hour for 3/2 hours and y miles per hour

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Math Expert
Joined: 02 Sep 2009
Posts: 55266
A vehicle averaged x miles per hour for 3/2 hours and y miles per hour  [#permalink]

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20 Mar 2018, 06:41
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Difficulty:

65% (hard)

Question Stats:

54% (01:47) correct 46% (01:46) wrong based on 97 sessions

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A vehicle averaged x miles per hour for 3/2 hours and y miles per hour for 5/2 hours on a nonstop trip of d miles. What was the average speed, in miles per hour, for the entire trip?

(1) x = y + 10
(2) d = 255

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Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: A vehicle averaged x miles per hour for 3/2 hours and y miles per hour  [#permalink]

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20 Mar 2018, 06:45
Bunuel wrote:
A vehicle averaged x miles per hour for 3/2 hours and y miles per hour for 5/2 hours on a nonstop trip of d miles. What was the average speed, in miles per hour, for the entire trip?

(1) x = y + 10
(2) d = 255

16. Distance/Rate Problems

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ALL YOU NEED FOR QUANT ! ! !
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Re: A vehicle averaged x miles per hour for 3/2 hours and y miles per hour  [#permalink]

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20 Mar 2018, 06:56
Bunuel wrote:
A vehicle averaged x miles per hour for 3/2 hours and y miles per hour for 5/2 hours on a nonstop trip of d miles. What was the average speed, in miles per hour, for the entire trip?

(1) x = y + 10
(2) d = 255

As this is a rate/time question, we'll need two out of rate, time and work to solve.
We'll look for a statement that gives us this information, a Logical approach.

We're given the speed as an equation with x and y, the total time ( = 3/2+5/2) and told that the distance is d.
To find out the speed, we need to know both x and y so we can calculate directly or d so we can calculate d/t

(1) this does not give us what we need.
Insufficient.

(2) we can now calculate distance/time = average speed.
Sufficient.

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Re: A vehicle averaged x miles per hour for 3/2 hours and y miles per hour  [#permalink]

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20 Mar 2018, 21:47
Bunuel wrote:
A vehicle averaged x miles per hour for 3/2 hours and y miles per hour for 5/2 hours on a nonstop trip of d miles. What was the average speed, in miles per hour, for the entire trip?

(1) x = y + 10
(2) d = 255

$$Average Speed = \frac{Total Distance}{Total Time}$$

From the stem we get

$$d = \frac{3x}{2}+\frac{5y}{2}$$
t = 4

Statement 1 : x = y+10 ----> This does not give us the value for total distance. Insufficient

Statement 2 : d=225 ------> We have total time from stem and total distance from statement 2 . Sufficient
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Re: A vehicle averaged x miles per hour for 3/2 hours and y miles per hour  [#permalink]

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03 Apr 2019, 05:49
Bunuel wrote:
A vehicle averaged x miles per hour for 3/2 hours and y miles per hour for 5/2 hours on a nonstop trip of d miles. What was the average speed, in miles per hour, for the entire trip?

(1) x = y + 10
(2) d = 255

speed x mph= 2d/3 and ymph= 2d/3
avg speed = 2d/4 = d/2
#1
no info of d insufficient
#2
d=225
sufficeint
IMO B
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Re: A vehicle averaged x miles per hour for 3/2 hours and y miles per hour   [#permalink] 03 Apr 2019, 05:49
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