How to prove going 75 mph for 1 mile makes it impossible to go another mile averaging 150 mph?

Question

If you go 75 mph for the 1st mile and x mph for the second to average 150 mph, x does not actually exist (except as infinity). How do I explain this?

Answer 1

It takes t amount of time to go 1 mile at 75 mph.  Because you are going twice as fast, it takes 1/2*t amount of time to go 1 mile at 75 mph.  Therefore, it takes t amount of time to go 2 miles at 150 mph.  Since you have already spend t amount of time going the first mile at 75 mph, you need to go the other mile without spending any time.

Answer 2

OK .. let's see

speed = distance / time

v = d /t

so ..

75 = 1 / t

t = 1/75 hours

so it takes 1/75 hours to travel a mile with a speed of 75 miles

to travel 2 miles with a speed of 150

150 = 2/t

t = 2/150

t = 1/75 hours

So ..

so it takes 1/75 hours to travel a mile with a speed of 150 miles

then if we travel for any additional distance it can't be taken in the same time of (1/75 hours)

so

x has to be infinity

Answer 3

(75 + x) / 2 = 150 , this is the average of the two miles, so multiply by 2 to both sides

75 + x = 300

x = 225 , seems to me that going 225 mph in the seconds mile would make it average to 150 mph

Answer 4

average velocity = total distance/total time

average velocity = 150 mph

total distance = 2 miles

time, first mile = 1/75 hr

time, second mile = 1/x hr

total time = 1/75 + 1/x hr

150 = 2/(1/75 + 1/x)

1/75 + 1/x = 2/150

1/75 + 1/x = 1/75

This will be true only if 1/x = 0, or if x is infinity.  Therefore x does not exist.

Answer 5

It's wrong. X=225 mph and it definitely does exist.

Answer 6

75 mph for 1 mile takes

1/75 or 0.0133 hr or 0.8 min

in order to go an average of 150 for 2 miles, it would take

2/150 = 0.8 min

But you have already used 0.8 min for the first mile, so that means the second mile would have to be done in 0 time, which is impossible.

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