Source: Official Guide for the GMAT 13th Ed. Problem Solving; #162 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #162

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# During a trip, Francince traveled x percent

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

### 3 Explanations

1

yousef aljamili

Hi,

I used "XD/100" for d1 and for the complement d2 I inputted "D - xD/100"

Although I understand Mike's explanation completely, can you please explain why it does not lead me to the correct answer when i use 'D-xD/100'

Sep 22, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Yousef :)

It is actually possible to use those values for d1 and d2 to solve this question :) One way is to consider that

average speed = D/(d1/v1 + d2/v2)

where

d1 = xD/100
v1 = 40
d2 = D - xD/100
v2 = 60

d1/v1 = xD/100/40 = xD/4000
d2/v2 = (D - xD/100)/60 = D/60 - xD/6000

d1/v1 + d2/v2 = xD/4000 + D/60 - xD/6000
= D/60 + xD/12000
= (200D + xD)/12000

D/(d1/v1 + d2/v2) = 1/(200D + xD)/12000
= 12000D/(200D + xD)
= 12000/(200 + x) --> Choice E

The calculation can get a little messy but as you can see, we can solve the problem in this way :)

Sep 23, 2016 • Reply

1

Daniel Farmer

At 3:36, Mike meant to say "12,000," not "200,000"

Nov 29, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Daniel!

Thank you all for letting us know about this! You're completely correct that Mike meant to say "12,000" instead of "200,000" at 3:36 in the explanation. So, I've sent a note to our content editors so that this can be fixed. However, since we have a very small team with lots to work, it may take a while for a new video explanation to be uploaded. In the meantime, thanks to your keen observation, other students will know about the mistake in the current explanation, which should hopefully avoid any confusion. Thanks again for your comment!

Cheers,

Cydney :)

Dec 2, 2015 • Reply

1

Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

Maria Chernaya

Wouldn't it be easier just to pick numbers and then test each answer choice? The numbers I picked were 240 miles for the total distance, and 50 percent for x. So during the first leg, Francine traveled 120 miles, at 40 mph, for 3 hours. The second leg, Francine would have traveled for 2 hours. And then I got 240 miles as the total distance over 5 hours, for an average speed of 48 mph. When you plug 50 into x into the last equation, you get 48.

Oct 2, 2015 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Maria,

Excellent point!

For this question, plugging in values does lead to a less complicated and most-likely quicker way to find the correct answer :) Mike actually compares the algebraic approach (which he uses in this explanation video) to plugging in to solve this problem on the following post from our GMAT blog: http://magoosh.com/gmat/2012/gmat-official-guide-practice-problem-francines-trip/

Again, great observation!

Cheers,
Cydney :)

Oct 25, 2015 • Reply