A car drove from Town A to Town B without stopping. The car traveled the first 70 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 90 miles if the car’s average speed for the entire trip was 40 miles per hour? Choose the correct choice from the following.
A) 28 B) 48 C) 50 D) 55 E) 75
KAPLANOFFICIAL SOLUTION:   To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.   For the first 70 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 70/25, because distance divided by rate equals time.   For the last 90 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 90 miles is 90/R.   If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(70/25 + 90/R) = 40. We can now solve for R and reach our answer.   160/(70/25 + 90/R) = 40   R = 75   75 is choice (75) and that’s our correct answer.
<result>E</result>
A car drove from Town A to Town B without stopping. The car traveled the first 70 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 90 miles if the car’s average speed for the entire trip was 40 miles per hour?