Can someone explain this physics problem?

So… for the first half of the journey the motorist is on track. At this point he has traveled 20 km and has spent 30 minutes doing it.

Now for the next 10 km he travels at 20km/h, which means that he spends another 30 minutes traveling that 10 km.

This means that the answer is D. Because the motorist has already been traveling an hour and has only covered 30km. Thus, to meet his goal the motorist must travel the last 10 km instantaneously.

If he wishes to travel 40km at 40km/h, that means he wants the journey to take a total of 1 hour. For the first 20km, he averages 40km/h. So the first 20km take 30 minutes. Next 10km, he averages 20km/h, so those 10km take him another 30 minutes. He’s already used up his entire hour. There is therefore no way to make the last 10km and still complete the journey within one full hour. The answer is therefore D.

I agree with the two above me, and here’s a mathmatical proof.

So first the motorist goes 20km at 40km/h, which means that leg of the journey must have taken half an hour (30 min). Then he goes 10km at 20km/h which would also take 30 min. To find the average speed, (even though it’s obvious in this case) you must do a weighted average. Half the time was spent at 40km/h, and the other half was spent at 20km/h, so use .5*40+.5*20 = 30km/h. So over this hour he has gone an average of 30km/h.

He wants to raise that average to 40km/h, and he has 10km in which to do so. Let’s call the speed he travels during the last 10km, x km/h. The time it will take him is 10/x h. So now the total time of the trip is .5 h + .5 h + 10/x h.
Your weighted average becomes (.5/(1+10/x))(40) + (.5/(1+10/x))(20) + ((10/x)/(1+10/x))(x)
Simplified: 20/(1+10/x) + 10/(1+10/x) + 10/(1+10/x) = 40/(1+10/x)
Note that this becomes 40 when the denominator becomes one. However, 1+10/x only equals 1 when 10/x = 0, which means that x must be approaching infinity for the average speed to be 40km/h.

Instantly is difficult, and not “faster than the speed of light.” Therefore, the answer is “E” use a time machine.

Variations of this problem have a long history. I was used at least once as the weekly “Puzzler” on the NPR show “Car Talk.”

The answers above are all correct.

Your physics “professor” couldn’t understand that? Is it too late to transfer to another class? Or school?

Thank you all for your answers!
My professor doesn’t speak terrific English, and I think the language barrier added to the confusion we were having.
I definitely understand now, and I will use your answers to help explain to my classmates.
Thanks!!