Question

On a long drive, a truck covered P percent of the total distance on local road, where it drove only 30 mph. The rest of the trip, it traveled at 50 mph. In terms of P, which of the following represents the average velocity of the entire trip?

(A) P−10

(B) 50−P/5

(C) (2P+1000)/40

(D) 10000/(P+200)
(E) 15000/(2P+300)

Answer 1

The average velocity of the entire trip in terms of P, where P represents the percent distance covered on the local road at 30 mph, is represented by (E) 15000/(2P+300). The correct answer is found by deriving an expression for total distance and total time and simplifying it.

Step-by-step explanation:

To find the average velocity of the entire trip in terms of P, where P represents the percentage of the distance covered on the local road at 30 mph, we need to establish a relationship between distance, speed, and time.

Let's assume the total distance of the trip is D. Then the truck travels (P/100) * D miles at 30 mph and the remaining ((100-P)/100) * D miles at 50 mph. Average velocity is defined as the total distance divided by the total time. Therefore, we must find the time taken for each portion of the trip and add them together for the total time.

The time to travel the P percent of the distance at 30 mph is (P/100) * D / 30, and the time to travel the remaining distance at 50 mph is ((100-P)/100) * D / 50. Adding these times gives us the total time T of the trip:

T = (P/100) * D / 30 + ((100-P)/100) * D / 50

Now, we can calculate the average velocity Vavg as follows:
Vavg = D / T = D /
[(P/100) * D / 30 + ((100-P)/100) * D / 50]

After simplifying this expression and canceling out the common factor of D, we find that the correct representation of the average velocity of the entire trip in terms of P is:

Vavg = 15000/(2P+300)

Therefore, the answer that represents the average velocity of the entire trip in terms of P is (E) 15000/(2P+300).