Tricky Rate Problem

[gmatassistance]

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?

[moliver]

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

[Stuart@KaplanGMAT]

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).

[Scott@TargetTestPrep]

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