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During a trip on an expressway, Don drove a total of x miles. His [#permalink]
27 Jan 2006, 16:35

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00:00

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E

Difficulty:

75% (hard)

Question Stats:

62% (03:26) correct
38% (03:09) wrong based on 385 sessions

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

During a trip on an expressway, Don drove a total of x miles [#permalink]
14 Aug 2006, 07:29

5

This post was BOOKMARKED

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5% B. 50% C. x/12% D. 60/x% E. 500/x%

Last edited by Bunuel on 07 Mar 2013, 04:20, edited 1 time in total.

Renamed the topic, edited the question and added the OA.

Re: During a trip on an expressway, Don drove a total of x [#permalink]
07 Mar 2013, 04:39

7

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Expert's post

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fozzzy wrote:

Whats the answer for this question and the best strategy for this question is to plug numbers or solve algebrically?

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5% B. 50% C. x/12% D. 60/x% E. 500/x%

For such questions I personally prefer plug in method. For this particular problem this method should give you the answer in less than a minute.

Say x = 5 miles (so no remainder of the trip).

Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes. Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/60 = 1/12 hours = 5 minutes.

(Or simply, half rate will result in doubling the time.)

So, we can see that the time to cover x = 5 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 5 miles at 60 miles per hour (5 minutes).

Now, plug x = 5 miles into the answer choices to see which one yields 100%. Only answer E works.

Re: During a trip on an expressway, Don drove a total of x miles [#permalink]
09 Mar 2013, 14:02

1

This post received KUDOS

I assumed x=10

time taken for 5 miles at 30mph = 10min time taken for the remaining 5 miles at 60mph = 5min total time taken to travel 10miles = 15min = T1

If travelled at 60mph constantly for the entire 10 miles then total time taken = 10min = T2

Percentage change in time = \(\frac{(T1-T2)}{T2}*100\) = 50%

Now this is just one of the answers, it is supposed to change if the total distance changes, as 5 miles becomes different fraction of the total distance (so answer must contain the total distance x, thereby eliminating choice A & B).

By plugging in with answer choices to see which results in 50% will get the answer i.e E

Re: During a trip on an expressway, Don drove a total of x miles [#permalink]
03 Jul 2013, 21:16

We can plug in any value for x because we can see that x is not tied to a specific value. Let us plug in a convenient value.

1. Assume x=10 miles. Total time taken when traveling at different speeds is 5/30 hr + x-5 /60 hr. = 5/30 hr + 5/60 hr = 10 min + 5min = 15 min 2. Total time taken at 60 miles /hr = (5 + x-5)/60 = 10/60 hr = 10 min 3. (1) greater than (2) by 50 %. 4. Substitute the assumed value of x in the choices . Only E gives 50 %

B is not correct because if you change the value of x, the percentage increase will change. _________________

Re: During a trip on an expressway, Don drove a total of x miles [#permalink]
05 Aug 2013, 11:04

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

The question is looking for how much longer it would take Don to complete the trip at slower speed + faster speed than just faster speed.

Formula for % increase of A over B:

100%*(A-B)/B = 100%*(A/B-1) = 100%(A/B) - 100%

Percentage change in time = (t1-t2)/t2 * 100%

I assume that we can set a number to x because we are looking for time and not distance.

x=10

30 miles/hour = .5 miles/minute t1=5/.5 t1=10

60 miles/hour = 1mile/minute t1=5/1 t1=5

So it took him 10 minutes to cover the first half and 5 minutes to cover the second half for a total of 15 minutes.

We are looking to compare how long it would take him to cover the distance of slow+fast vs. just fast. If he covered the entire 10 miles at 60 miles/hour he would have spent 10 minutes on the road.

Percentage change in time = (t1-t2)/t2 * 100% (15-10)/10 * 100% 5/10 * 100% .5*100% = 50%

He would have traveled 50% faster if the entire journey was completed at 60 miles/hour.

Now plug x into the answer choices to see which one matches.

Re: During a trip on an expressway, Don drove a total of x miles [#permalink]
31 Oct 2014, 02:43

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Re: During a trip on an expressway, Don drove a total of x miles. His [#permalink]
21 Jul 2015, 10:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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During a trip on an expressway, Don drove a total of x miles [#permalink]
22 Jul 2015, 06:54

Expert's post

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5% B. 50% C. x/12% D. 60/x% E. 500/x%

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During a trip on an expressway, Don drove a total of x miles
[#permalink]
22 Jul 2015, 06:54

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