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# During a trip, Francine traveled x percent of the total

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Manager
Joined: 08 Apr 2004
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During a trip, Francine traveled x percent of the total [#permalink]

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05 Sep 2004, 07:17
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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 Francineâ€™s average speed for the entire trip?

180-x/2

x+60/2

300-x/5

600/115-x

1200/x+200

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Director
Joined: 20 Jul 2004
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05 Sep 2004, 09:52
I got 12000/(x+200).
Could E be a typo missing a zero?

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Manager
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05 Sep 2004, 12:33
Hey guys can you explain your answers i am kind of lost .
_________________

---- Hero never chooses Destiny
Destiny chooses Him ......

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Intern
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05 Sep 2004, 14:20
i am with hardworking on this one. I think the individual who posted forgot to include the final zero on answer E. I plugged in and said that the traveler drove 50%,x, of 120 miles trip at 40 mph and the other half at 60 mph. Therefore the total traveling time was 2.5 hours for 120 miles and the average speed was 48 mph. C comes close but if you add another zero to E, then 250x48=12,000.

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Manager
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05 Sep 2004, 16:09
Actually, none of the answers is correct.

The correct answer is 120/(x + 2).

Here's the derivation:

Suppose total distance travelled is 1 mile. Then, x and (1-x) become actuall distances travelled and not just percentages.

Total distance travelled = S = x + 1 - x = 1

Total time taken = t = (x/40 mph) + [(1-x)/60 mph] = (3x + 2 - 2x) / 120 = (x+2)/120

Average speed = S / t = 1 / [(x+2)/120] = 120/(x+2)

The other suggested answer: 12000/(x+200) will not work, as x is in percentages/proportions and not actual units.

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Director
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06 Sep 2004, 09:31
I stay corrected at 12000/(x+200).

My explanation:
Let the total distance traveled be A.
First Section: Distance = xA/100, Speed = 40, Time = xA/4000
Second Section: Distance = A(100-x)/100, Speed = 60, Time = A(100-x)/6000

Total journey: Distance = A, Time = [xA/4000+ A(100-x)/6000]
Ave. Speed = [A] / [xA/4000+ A(100-x)/6000]
= 12000/(x+200).

Recheck:
For checking back, lets say he travelled a total distance of (A=) 60 miles, and x = 25%
First Section: Distance = 15, Speed = 40, Time = 15/40
Second Section: Distance = 45, Speed = 60, Time = 45/60
Total journey: Distance = 60, Time = 135/120, Ave. Speed = 160/3
Substitute x=25 in 12000/(x+200), you get 160/3

PS:
I had initially taken total distance to be 100 for simplicity in calculation. But took a generic distance of A, just to prove the point.

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Manager
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06 Sep 2004, 10:15
Well, you're assuming x to be in 100 percentage points. Although that's not what the question said, as long as you're explicitly saying that x is in 100 percentage point, your formula will be correct.

You can get my formula from yours by noticing that x is in 100 percentage points in your formula and dividing the numerator and denominator by 100. My formula is in percent/proportions. That's the only difference.

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Manager
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06 Sep 2004, 16:40
abennett wrote:
i am with hardworking on this one. I think the individual who posted forgot to include the final zero on answer E. I plugged in and said that the traveler drove 50%,x, of 120 miles trip at 40 mph and the other half at 60 mph. Therefore the total traveling time was 2.5 hours for 120 miles and the average speed was 48 mph. C comes close but if you add another zero to E, then 250x48=12,000.

OOPS!, my mistake , yes it is 12000 and the answer is E infact (1200/x+200)

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06 Sep 2004, 16:40
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