I travel up a 1 mile hill at 30 mph?
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?
Answers:
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.
90 miles per hr because average speed=total distance/total time
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.
90
90mph
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
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.
the question is vague. it will have to be reworded properly to be able to answer the question.
If time and distance covered is irrelevent, then the simplest answer is 90mph.
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
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.
Cannot be done, you've used up all your time going up.
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.
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Answers:
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.
90 miles per hr because average speed=total distance/total time
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.
90
90mph
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
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.
the question is vague. it will have to be reworded properly to be able to answer the question.
If time and distance covered is irrelevent, then the simplest answer is 90mph.
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
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.
Cannot be done, you've used up all your time going up.
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.
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