Dwllane4

2022-06-21

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?

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?

Carmelo Payne

Beginner2022-06-22Added 25 answers

We have ${v}_{1}=20,{d}_{1}=25,{d}_{2}=25$

We want $40={\displaystyle \frac{{d}_{1}+{d}_{2}}{{d}_{1}/{v}_{1}+{d}_{2}/{v}_{2}}}={\displaystyle \frac{50}{25/20+25/{v}_{2}}}$ (that is: total distance divided by total time).

Hence we need indefinite speed. ${v}_{2}={\displaystyle \frac{25}{50/40-25/20}}={\displaystyle \frac{25}{0}}$

We want $40={\displaystyle \frac{{d}_{1}+{d}_{2}}{{d}_{1}/{v}_{1}+{d}_{2}/{v}_{2}}}={\displaystyle \frac{50}{25/20+25/{v}_{2}}}$ (that is: total distance divided by total time).

Hence we need indefinite speed. ${v}_{2}={\displaystyle \frac{25}{50/40-25/20}}={\displaystyle \frac{25}{0}}$

kokoszzm

Beginner2022-06-23Added 8 answers

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.