Problem Solving

A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per
hour. At what average speed must the driver complete the remaining 20 miles to achieve
an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver
did not make any stops during the 40-mile trip.)

A. 65 mph
B. 68 mph
C. 70 mph
D. 75 mph
E. 80 mph

Let me try to help you out. This is my first time try to help someone out here. This is what I got for this question.

First you find the mins for 60mph for 40miles.

60(x)=40
x=.66666667

Since they never ask about the time this is my set up for the next part

((50+y)/2)(.6666667)=40
y=70

So the answer should be C.

I guess you can assume 50mph for 20 miles and 70 mph for another 20 miles would give you 60mph for 40 miles.

We can solve this question by setting up a chart and using the formula Average speed = total distance/total time, or by using the "round trip" formula:

Average speed = (2*speedx*speedy)/(speedx + speedy)

in which speed x is the speed for one leg of the journey and speed y the other. It is important to note that you can use this formula only when the two legs of the journey are equidistant (that's why we can call it the "round trip" formula).

Here, we know that the legs of the journey are equal in distance (each is 20 miles), and so we can use this formula. We want the average speed to be 60, and we know that one of the speeds is 50. Let's call the other speed "x". So we have:

60 = (2*50*x)/(50+x)

and, solving for x, we have x = 75.

Choose D.


(Unfortunately, pkan, you fell into a common trap with average speed problems: you assumed the average speed of the whole trip is simply the mathematical average of the two speeds. However, average speed is actually a weighted average concept. Travelling at a slower speed means that it will take you a longer amount of time to cover any given amount of distance. Thus, when you have an object whose journey is divided into two equally long legs, the slower speed will contribute more to the average speed than will the faster speed.)

deepak123gmat wrote:A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per
hour. At what average speed must the driver complete the remaining 20 miles to achieve
an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver
did not make any stops during the 40-mile trip.)

A. 65 mph
B. 68 mph
C. 70 mph
D. 75 mph
E. 80 mph

We could plug in the answer choices, which represent the speed for the remaining 20 miles.

The correct answer must be more than 70. If we travel for 20 miles at 70 mph after traveling the first 20 miles at 50 miles per hour, the average for the whole trip will not be (50+70)/2 = 60 (the number right in the middle) because we won't spend the same amount of time traveling at each speed. Since we'll spend more time traveling at 50mph than we'll spend traveling at 70mph, the average for the whole trip will be closer to 50 than to 70. Thus, in order for the average for the whole trip to be 60, we must travel faster than 70mph for the remaining 20 miles. Eliminate A, B and C.

Let's try answer choice D:
d/r = 20/75 = 4/15 hour for the remaining 20 miles
d/r = 20/50 = 2/5 hour for the first 20 miles
Total time = 4/15 + 2/5 = 10/15 = 2/3 hour
Total distance = 20+20 = 40 miles
Average speed = d/t = 40/(2/3) = 60mph

The correct answer is D.

Thanks a ton.
That was gr8.