Rate problem

OA may skip important details see my solution below

D=distance, Speed=S, T=time; xD/100 at average S(1)=40; (100-x)D/100 at average S(2)=60; find D/(T1+T2)-?
T1=xD/100 : 40 and T2=(100-x)D/100 :60; T1+T2=[3xD+2D(100-x)]/(100*120)= (xD+200D)/(100*120)

D: (xD+200D)/(100*120)= 12000/(x+200)

garuhape wrote: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 the average speed for the entire trip.

Official Answer: 12000/(x+200)

I don't understand the solution.

I did it like that:

x*40+(1-x)*60=average speed of total trip. <--- it says precisely x% but we don't know the value of x, e.g. x=20% you take 1-20 which is -19, but should be x%=x/100 and (100-x)/100

Let's say that she traveled 30% of the distance at an average speed of 40 and 70% at an average speed of 60. Thus the average speed of the total trip is:

0.3*40+0.7*60=54

:

GMATGuruNY wrote: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?

a. (180-X)/(2)
b. (x+60)/(4)
c. (300-x)/(5)
d. (600)/(115-x)
e. (12,000)/(x+200)

Plug in a value for the distance and a value for x.

Let distance = 100 miles.
Let x = 40.
Distance for 40% of the trip = .4*100 = 40 miles.
Since the rate for this portion is 40mph, time = d/r = 40/40 = 1 hour.
Distance for remainder of the trip = 100-40 = 60 miles.
Since the rate for this portion is 60mph, time = d/r = 60/60 = 1 hour.
Total time = 1+1 = 2 hours.
Average speed for the whole trip = (total distance)/(total time) = 100/2 = 50. This is our target.

Now we plug x = 40 into all the answer choices to see which yields our target of 50.

Only answer choice E works:
(12,000)/(x+200) = 12000/(40+200) = 50.

The correct answer is E.[/quote]

Using what you have written in blue

x/100*40 + (100-x)/100*60 = 40x/100+60(100-x)/100 = 40x/100+(6000-60x)/100 = (6000-20x)/100 = (300-x)/5,

which is one of the answer choices but which apparently is wrong. However, if you try it out the formula works perfectly fine.

Thanks guys, now I understood it