I travel up a 1 mile hill at 30 mph?

Question

I travel up a 1 mile hill at 30 mph. How fast must I go down the 1 mile on the other side to average 60 mph for the complete hill?

I'm surprised how many people got caught out with this question.

Answer 1

There are two methods to find the answer to this:

1st method:
To average a speed of 60mph over the complete hill which is two miles in distance, you would need to take 1/30th of an hour to travel up and down the hill, which is 2 minutes (time=distance/speed).

You have travelled up the 1 mile hill at a speed of 30 mph, so the time you have taken would be 1/30th hour, which is 2 minutes (t=d/s).

Because you would need to take 2 minutes to travel the full 2 miles and the 1st mile has already taken 2 minutes, you would need to cover the remaining mile instantaneously. So the speed for the second mile would need to be 1/0 (speed=distance/time), therefore you would need to be travelling at an infinitely fast speed to average 60 mph for the complete hill. So in practice it is impossible to average 60 mph.

You can easily check this, even if you travelled the second mile at 600 mph, the second mile would take 1/600th of an hour which is 0.1 minutes. So the total time taken to travel 2 miles would be 2.1 minutes giving an average speed of 57 mph.

2nd method:
speed = distance / time
if you let x be the time taken for the 2nd mile, and the time taken for the 1st mile is 1/30th hour, then for the complete hill,

60 = 2 / ( 1/30 + x)

solving this gives x = 1/30 - 1/30 = 0
so the 2nd mile must be travelled instantaneously, therefore at an infinitely speed, so it is impossible to average 60 mph in practice.

Answer 2

First, 30 mph is an average. You could do any velocities and average 30 mph. For instance, the first 1/4 mile could have a velocity of 20, the second 40, the third 10 and the fourth at 50. So to get 60 mph from two averages you would need the formula ((30+X)÷2)=60, then (((30+X)÷2)×2)=60×2. Next 30+X-30=120-30 and then X=90. That would give an average of 60 mph. If you want bring in 1 mile up the hill and one mile down and an average of 60 mph for both sides you must do 60 mph from the beginning. You can not mix velocity with speed one is an average of the other.
You could say Ken drove 5 miles in one hour and then another 10 miles in one hour, what was his average speed after 10 miles. It would be 5mph plus 10mph divided by 2 equals an average of 7.5 miles per hour. And had he driven 7.5 mph from beginning to end, he would still have driven 15 miles in 2 hours. You can stop in the middle and demand the second half to now cover the beginning, middle, and end.

Answer 3

I travel up the hill 1 mile at 30 MPH. (taking 2 minutes)

travelling 2 miles at an average of 60MPH takes 2 minutes.

so you would need a time travel machine to get to the end in 0 seconds to average 60mph over the 2 mile journey.

Answer 4

It can't be done. You would take 2 minutes to go up the hill at 30 mph. To go 60 mph across the whole hill, it would be 2 miles / (60 mph) * 60 min/hr = 2 minutes. You've already used your 2 minutes. In theory, if you could travel at an infinate speed, you could do it.

Answer 5

It would take you 2 minutes to go up the hill. You need to cover the entire 2 miles in 2 minutes to average 60 MPH. So you would not be able to do it. But if you went an extra mile and did it in one minute (1 mile down hill plus one more mile), you would have averaged 60MPH because you covered 3 miles in 3 minutes.
Funny thing about averages.

Answer 6

It's not possible. To average 60 mph over 2 miles, you need to make the trip in 2/60 hours, or 2 minutes.

But you took 1/30 hours=2/60 hours=2 minutes to travel the first mile. So you would have to travel the second mile instantaneously.

Answer 7

since the 1st mile is travelled in 30 mph the second should be travelled at a distance of about 90mph to make an average of 60mph

Answer 8

a million hour = 60 minutes the motor vehicle made sixteen miles in half-hour, that's a million/2 of 60 minutes. as a result the motor vehicle will do yet another sixteen miles interior the relax half-hour assuming a relentless speed. So it rather is vacationing at 32 miles in line with hour.

Answer 9

90

Answer 10

although you would have to go 90 the second half of your journey in order to AVERAGE 60.
You can not do it in the way the question is worded.
MPH is different than just numbers like 30,60,90