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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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Difficulty:
85% (hard)
Question Stats:
61% (03:26) correct
39% (03:03) wrong based on 527 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.
During a trip on an expressway, Don drove x miles.His average speed on [#permalink]
11 Dec 2010, 17:11
1
This post was BOOKMARKED
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile seciton was 30 miles per hour and his average speed of the remainder ofthe 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 travelled at a constant rate of 60 miles per hour for the entire trip
Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]
11 Dec 2010, 19:37
1
This post received KUDOS
Yellow22 wrote:
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile seciton was 30 miles per hour and his average speed of the remainder ofthe 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 travelled 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%
Long word problem with a variable in the choices - perfect situation for picking numbers.
Let's let x=15 to keep things simple.
So, he drove 5 miles at 30mph and 10 miles at 60mph.
time = dist/rate, so he spent 5/30 + 10/60 = 1/6 + 1/6 = 1/3 of an hour = 20 minutes total.
If he had travelled at 60mph for the entire 15 miles, his time would have been 15/60 = 1/4 hour = 15 minutes.
The question is "His travel time for the x mile trip was what percent greater", so we use the percent change formula:
% change = (amount of change / original amount) * 100%
Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]
22 Feb 2011, 14:28
Time when droven x miles in 60 mph \(t1\)= \(x/60\) time when droven 5 miles in 30mph and x-5 miles in 60mph \(t2\)= \(5/30\) + \((x-5)/60\) = \((x+5)/60\)
Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]
22 Feb 2011, 14:49
I think the question should be:
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile section was 30 miles per hour and his average speed of the remainder ofthe trip was 60 miles per hour. His travel time for the x mile trip was what percent smaller than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip
Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]
22 Feb 2011, 15:24
fluke wrote:
I think the question should be:
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile section was 30 miles per hour and his average speed of the remainder ofthe 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
Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]
22 Feb 2011, 15:31
maddy2u wrote:
fluke wrote:
I think the question should be:
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile section was 30 miles per hour and his average speed of the remainder ofthe 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
Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]
08 Mar 2011, 18:39
Let x = 15 5 miles @ 30 mph time = 1/6 10 miles @ 60 mph time = 1/6 Total time = 1/3 15 miles @ 60 mph, time = 1/4 % change (1/3 - 1/4) /1/4 = 1/3 or 100/3% = 33.33%
Re: During a trip on an expressway, Don drove a total of x [#permalink]
07 Mar 2013, 04:39
10
This post received KUDOS
Expert's post
5
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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
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