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a little math problem

Random Variable

Random Variable

Lifer
The distance from point A to point B is 100 miles. If you average X mph for the first fifty miles, what speed would you have to average for the second 50 miles so that your average speed for the entire trip is 2X mph?
 
Wait, no that's not right

OK, I'm confident it's not possible. You'd have to complete the second half of the trip instantaneously.

Suppose you complete the first half of the trip in 1 hour at 50 mph. You'd then have to adjust your speed to finish with an average speed of 100 mph. You have to travel a total distance of 100 miles in a total time of 1 hour, and you've already used your whole hour.
 
Originally posted by: mugs
Wait, no that's not right

OK, I'm confident it's not possible. You'd have to complete the second half of the trip instantaneously.

Suppose you complete the first half of the trip in 1 hour at 50 mph. You'd then have to adjust your speed to finish with an average speed of 100 mph. You have to travel a total distance of 100 miles in a total time of 1 hour, and you've already used your whole hour.
Click to expand...

lol, are you serious
 
Originally posted by: Inspector Jihad
Originally posted by: mugs
Wait, no that's not right

OK, I'm confident it's not possible. You'd have to complete the second half of the trip instantaneously.

Suppose you complete the first half of the trip in 1 hour at 50 mph. You'd then have to adjust your speed to finish with an average speed of 100 mph. You have to travel a total distance of 100 miles in a total time of 1 hour, and you've already used your whole hour.
Click to expand...

lol, are you serious
Click to expand...

Post your answer.
 
Topic Title: a little spelling problem
Topic Summary: I'm embarrassed that I didn't know the answer instanteously



fixed.



 
Originally posted by: mugs
Wait, no that's not right

OK, I'm confident it's not possible. You'd have to complete the second half of the trip instantaneously.

Suppose you complete the first half of the trip in 1 hour at 50 mph. You'd then have to adjust your speed to finish with an average speed of 100 mph. You have to travel a total distance of 100 miles in a total time of 1 hour, and you've already used your whole hour.
Click to expand...

Wait, no.
 
Originally posted by: Random Variable
The distance from point A to point B is 100 miles. If you average X mph for the first fifty miles, what speed would you have to average for the second 50 miles so that your average speed for the entire trip is 2X mph?
Click to expand...

Infinity
 
obviously impossible, unless you are screwing around with the semantics

straightforward interpretation of the problem,
100/(2x) = 50/x + 50/y
50/x = 50/x + 50/y
0 = 50/y
 
Originally posted by: Mike2002
I'd have to say 3X as well.
Click to expand...

Suppose he drove 50 mph for the first 50 miles. That's 1 hour.

Then he drove 150 mph for the second 50 miles. That's 20 minutes.

So he drove 100 miles an an hour and 20 minutes, for an average speed of 75 mph.

50mph * 2 = 100 mph. Drive faster!
 
Originally posted by: 91TTZ
Originally posted by: mugs
Wait, no that's not right

OK, I'm confident it's not possible. You'd have to complete the second half of the trip instantaneously.

Suppose you complete the first half of the trip in 1 hour at 50 mph. You'd then have to adjust your speed to finish with an average speed of 100 mph. You have to travel a total distance of 100 miles in a total time of 1 hour, and you've already used your whole hour.
Click to expand...

Wait, no.
Click to expand...

Que?
 
Hey, I have an idea:

What if you linearly accelerated from 0 to infinity MPH during the first leg of the trip. The second leg of the trip would be traveled at infinity MPH, meaning no additional time.
 
Originally posted by: bonkers325
3X
Click to expand...

Originally posted by: Mike2002
I'd have to say 3X as well.
Click to expand...

Originally posted by: 91TTZ
No, you have to go the second leg at 150 mph
Click to expand...

Average speed = distance / time

First 50 miles @ X MPH
Distance: 50 miles
Time: 50 miles / X mph

Second 50 miles @ 3X mph
Distance: 50 miles
Time: 50 miles/ 3X mph

Total trip
Average Speed = (50 miles + 50 miles) / (50 miles / X mph + 50 miles / 3X mph)
Simplify numerator, find common denominator in denominator
= 100 miles / ((150 miles + 50 miles) / 3X mph)
= 100 miles / (200 miles/3X mph)
= 1.5X MPH

So as I said before, the answer is infinity or rather, that it can't be done
 
Originally posted by: mugs
Originally posted by: Inspector Jihad
Originally posted by: mugs
Wait, no that's not right

OK, I'm confident it's not possible. You'd have to complete the second half of the trip instantaneously.

Suppose you complete the first half of the trip in 1 hour at 50 mph. You'd then have to adjust your speed to finish with an average speed of 100 mph. You have to travel a total distance of 100 miles in a total time of 1 hour, and you've already used your whole hour.
Click to expand...

lol, are you serious
Click to expand...

Post your answer.
Click to expand...

read the question wrong.
 
Originally posted by: b0mbrman
Originally posted by: bonkers325
3X
Click to expand...

Originally posted by: Mike2002
I'd have to say 3X as well.
Click to expand...

Originally posted by: 91TTZ
No, you have to go the second leg at 150 mph
Click to expand...

Average speed = distance / time

First 50 miles @ X MPH
Distance: 50 miles
Time: 50 miles / X mph

Second 50 miles @ 3X mph
Distance: 50 miles
Time: 50 miles/ 3X mph

Total trip
Average Speed = (50 miles + 50 miles) / (50 miles / X mph + 50 miles / 3X mph)
Simplify numerator, find common denominator in denominator
= 100 miles / ((150 miles + 50 miles) / 3X mph)
= 100 miles / (200 miles/3X mph)
= 1.5X MPH

So as I said before, the answer is infinity or rather, that it can't be done
Click to expand...

I edited my response 7 minutes before you even replied. I have a new answer.
 
Originally posted by: 91TTZ
Originally posted by: b0mbrman
Originally posted by: bonkers325
3X
Click to expand...

Originally posted by: Mike2002
I'd have to say 3X as well.
Click to expand...

Originally posted by: 91TTZ
No, you have to go the second leg at 150 mph
Click to expand...

Average speed = distance / time

First 50 miles @ X MPH
Distance: 50 miles
Time: 50 miles / X mph

Second 50 miles @ 3X mph
Distance: 50 miles
Time: 50 miles/ 3X mph

Total trip
Average Speed = (50 miles + 50 miles) / (50 miles / X mph + 50 miles / 3X mph)
Simplify numerator, find common denominator in denominator
= 100 miles / ((150 miles + 50 miles) / 3X mph)
= 100 miles / (200 miles/3X mph)
= 1.5X MPH

So as I said before, the answer is infinity or rather, that it can't be done
Click to expand...

I edited my response 7 minutes before you even replied. I have a new answer.
Click to expand...

Not quick enough for me to not catch it though
 
Originally posted by: b0mbrman
Originally posted by: 91TTZ
Originally posted by: b0mbrman
Originally posted by: bonkers325
3X
Click to expand...

Originally posted by: Mike2002
I'd have to say 3X as well.
Click to expand...

Originally posted by: 91TTZ
No, you have to go the second leg at 150 mph
Click to expand...

Average speed = distance / time

First 50 miles @ X MPH
Distance: 50 miles
Time: 50 miles / X mph

Second 50 miles @ 3X mph
Distance: 50 miles
Time: 50 miles/ 3X mph

Total trip
Average Speed = (50 miles + 50 miles) / (50 miles / X mph + 50 miles / 3X mph)
Simplify numerator, find common denominator in denominator
= 100 miles / ((150 miles + 50 miles) / 3X mph)
= 100 miles / (200 miles/3X mph)
= 1.5X MPH

So as I said before, the answer is infinity or rather, that it can't be done
Click to expand...

I edited my response 7 minutes before you even replied. I have a new answer.
Click to expand...

Not quick enough for me to not catch it though
Click to expand...


My new answer is:


What if you linearly accelerated from 0 to infinity MPH during the first leg of the trip. The second leg of the trip would be traveled at infinity MPH, meaning no additional time.

 
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