Tricky Rate Problem

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gmatassistance: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Jul 26, 2009 3:42 pm; Thanked: 1 times

by gmatassistance » Sun Apr 25, 2010 1:24 pm

A car averages 40 miles per hour for the first 6 hours of a trip and averages 60 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 55 miles per hour, how many hours long is the trip?

A) 8
B) 12
C) 16
D) 18
E) 24

Is there a quick and easy way to solve this problem in 2mins?

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Source: Beat The GMAT — Problem Solving | Sun Apr 25, 2010 1:24 pm

moliver: Senior | Next Rank: 100 Posts; Posts: 63; Joined: Wed Jul 16, 2008 6:43 am; Thanked: 3 times; GMAT Score:680

by moliver » Sun Apr 25, 2010 1:39 pm

is the OA E ?
Thanks

Average Speed = total distance / total time

55= (40*6 + 60*t )/(6 + t)
moving things you should get something like this:

5 t = 6*(55-0)
so t = 18
answer 18 + 6 = 24
I think the solution takes less than 2 min
please let me know if I didn't explain well

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sun Apr 25, 2010 1:51 pm

gmatassistance wrote:A car averages 40 miles per hour for the first 6 hours of a trip and averages 60 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 55 miles per hour, how many hours long is the trip?

A) 8
B) 12
C) 16
D) 18
E) 24

Is there a quick and easy way to solve this problem in 2mins?

Hi,

We have a word problem with a concrete ending (avg spd = 55) and answer choices that are simple numbers, so we should certainly be able to backsolve this problem in well under 2 minutes.

First, let's use some common sense to eliminate choices:

if it was 6 hours at 40 and 6 hours at 60, the average would be 50. The average is more than 50, so we need to spend more than another 6 hours driving to push the average closer to 60. Therefore, the total time is more than 12: eliminate (A) and (B).

Now that we have 3 choices left, we simply plug in the middle one and see what happens!

If the total journey is 18 hours, then:

Average speed = total distance/total time

= (6*40 + 12*60)/(6+12)

= (240 + 720)/18

= 960/18

= 480/9

= 160/3

which is less than 55. So, we need more time: eliminate (C) and (D), choose (E).

We could also solving this using a variation of the weighted average ratio. In pretty much any case in which you have an overall average and two sub-averages, we can set up the following ratio:

Group1 ----- x------- Overall Avg -------y--------Group2

Group1/Group2 = y/x

In this question:

40 ---- x----- 55 --y--60

Here, x is 15 and y is 5. 15/5 = 3/1, which means that we spend 3 times as long at 60mph as we do at 40mph.

So, 3 * 6 hours = 18 hours for the second part of the trip; 6 + 18 = 24... choose (E).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jul 04, 2018 6:28 pm

gmatassistance wrote:A car averages 40 miles per hour for the first 6 hours of a trip and averages 60 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 55 miles per hour, how many hours long is the trip?

A) 8
B) 12
C) 16
D) 18
E) 24

We can let the additional number of hours = t and create the following equation using the average rate formula:

Average rate = total distance/total time

55 = (40(6) + 60t)/(6 + t)

55(6 + t) = 240 + 60t

330 + 55t = 240 + 60t

90 = 5t

18 = t

Thus the total number of hours for the trip is 6 + 18 = 24.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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