Quick math/physics question?

Question

I know this question is supposed to be relatively easy, but I just can't seem to get the answer?? Am I thinking too hard?

2 cars are in a 2 mile race. The 2 cars start at the same time. Car A finishes the race with an average speed of 60 mph. Car B is averaging 30 mph at the 1 mile mark. What speed does Car B need to average for the rest of the race to beat Car A to the finish line?

For some reason I thought it was 90 mph...but I'm not sure.

Thanks for helping!

Answer 1

I am not to sure but if you add 30 + 90 then you will get 120. Divide 120 by 2 (2miles) and that will give you 60mph.

*The question does state BEAT so I would say >90mphs.

* Might be wrong but I know its in that direction.

Answer 2

2mi/60mph = 1mi/30mph+1mi/x

0 = 1/x

Thats the math part ... now the physics part.

If car b could instantaneously accelerate to the speed of light at the one mile mark effectively stopping time then he would tie car a at the finish.  If that is not possible then car b is guaranteed a loss.

Answer 3

If car A averages 60 mph, then on average it covers 1 mile in 1 minute.

Therefore it covered the 2 mile race in 2 minutes.

If car B averages 30 mph, that is a mile in 2 minutes

So when A finishes the race, B is at halfway ( both have taken 2 minutes.)

It is therefore impossible for B to win.

It would have to travel the remaining mile in no time at all!!.

Are you sure the numbers in the question are correct??

Answer 4

Read the explanation of the Harmonic Mean [link 1], which explains it.

There's a difference between "averaging 30pmh over a certain distance" and "during a certain time."

Anyway, applying the basic equation:

Distance (s) / Time (t) = Speed (v)

i.e. Time (t) = Distance (s) / Speed (v)

>Car A finishes the race with an average speed of 60 mph.

tA = (Distance) 2 / 60 (Speed) = 1/30 hr = 2min

>Car B is averaging 30 mph at the 1 mile mark.

Time of car B to 1=mile mark:

tB1 = (Distance) 1 / 30 (Speed) = 1/30hr = 2min.

Thus, when car A crosses the finish line, car B is only at the halfway mark!

>What speed does Car B need to average for the rest of the race to beat Car A to the finish line?

According to the above, when car A is crossing the finish line, car B is only at the halfway mark. Thus car B could not win even if went infinitely fast over the second mile (in which case it would draw, and that's impossible anyway).

[Footnote to EngiNerd: the speed of light is still not "infinitely fast", it's still only 3E8 meters/sec so it still loses. And yes, objects cannot move faster than the speed of light (where they acquire infinite mass-energy). Thus car B must lose.]