Problem

An automobile testing organization runs cars around a speed track to test performance. One test involves running a car around a 1200-meter track at high speed, and recording the individual lap times and the average speed for the entire test. On one occasion, the results are recorded, but are missing the final lap time. The first 4 laps show times of 37 seconds, 25 seconds, 29 seconds, 27 seconds, and the average speed for the test is recorded as 112 miles per hour.

Show that even without knowing the final lap time, we can conclude an error has most likely been made in recording the results.

Solution

Here are the average speeds for the first four laps, according to the recorded results.

We converted to miles per hour using the conversions 1 mile = 1609.344 meters, 1 hr = 3600 seconds. To convert from meters per second to miles per hour, multiply by 3600/1609.344 = 2.237.

Since we know the total distance of the test and the average speed according to the recorded results, we can find the total time the car takes to complete the test.

Therefore, the time needed for the final lap is

If this is correct, the car's average speed on the final lap is a whopping

This is highly unlikely, if the first four laps were run at the highest safe speed possible. Therefore we can conclude that there is probably some mistake in the numbers, even though we cannot determine which part of the results is incorrect.