ronr34 wrote:

Bunuel wrote:

summer101 wrote:

A car traveled 75% of the way from town A to town B at an average speed of 50 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?

A. 10

B. 20

C. 25

D. 30

E. 37.5

Say the entire distance is 200 miles.

75% of the distance = 150 miles.

25% of the distance = 50 miles.

Total time = 200/40 = 5 hours;

Time spent to cover 150 miles = 150/50 = 3 hours.

Thus 50 miles was covered in 5-3=2 hours --> S = (speed) = (distance)/(time) = 50/2 = 25 miles per hour.

Answer: C.

I tried to solve it a different way... using weighted averages but hit a wall...

Can you see where my logic fails?

Since the first part of the trip was 3/4 and the last was 1/4, this is what I got in my diagram:

S-----40-----50

----1-----3-----

When doing the cross multiplication, I get (50-40)/(40-S) = 3/1 -> I get S=110/3.

Why is this failing?

The weight when calculating average speed is time, not distance. This means that when you write (50-40)/(40-S) = 3/1, you are assuming that the car traveled 75% of the TIME at speed S and 25% of the time at speed 50 mph.

Ratio of 'Distance traveled' cannot act as the weight. See this post for a discussion of this concept:

bill-travels-first-40-of-the-distance-to-his-destination-at-137000.html#p1172411For this question, use the regular formula:

Avg Speed = Total Distance/Total Time \(= \frac{100}{75/50 + 25/S} = 40\)

This gives S = 25 mph

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Karishma

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