Measurement Question Related to a Race Car I recently got this peculiar interview question, and I wanted some help figuring
out how to reach an appropriate solution. Imagine that we have a race car that
is driving on a $50$-mile-long race track, and this race car has five minutes
to drive along this race track. Suppose that I went 20 miles per hour on the
first half of the race track. How fast do I need to go on the second half of the
race track such that I average 40 miles per hour over the whole drive on the
track?
I immediately went for the idea that the answer was 60 miles per hour, but
supposedly that was wrong. I think I needed to better consider the fact that
miles per hour is a measure of distance over time. So
$$40 \text{mph} = \frac{40 \text{ miles}}{60 \text{ minutes}},$$
But I am now stuck on how to use this information to deduce how many minutes
I need to take on the second half to average this speed. Any suggestions?

This wouldn't work. The first 25 miles he does it at 20mph. It would take him over an hour so its over the 5 minutes.
