You are driving by car to a particular destination, and the only assumption is that you are free to drive at any speed you choose - no traffic jams or anything like that. For the first half of the journey (i.e.half the distance) you drive at 20 miles per hour. You then realise that this is all taking much too long, and that you are going to be late. You therefore decide that you will increase your speed so that your overall average speed for the whole journey will be 40 miles per hour. How fast do you have to drive for the remaining part of your journey in order for your average speed for the whole journey to be 40 miles per hour?
don't worry about the petrol
- Thread starter kendor
- Start date
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kendor said:
if it's half and half, 60?
I was wondering this the other day, driving through some long distance speed cameras on the stocksbridge bypass, for the first half mile or so, i was doing 45, stuck behind a lorry, then i passed it, about another mile and a half to go before the next camera, the limit is 60, how fast could i travel so my average was 60? Those who think the limit is 50 do my head in, as do those who brake for the cameras, which don't actually measure instantaneous speed
Can't do it unless you teleport to your end destination from the half-way point......
e.g lets say the distance you are travelling is 40 miles.
The first 20 miles takes you one hour to do.
To average 40 miles an hour, you would have to travel 40 miles in one hour, or 80 miles in two, but you only have 40 miles total to go at, and you've already used your hour up, so you would have to do the second half in zero time.
Same works for all other distances....
e.g lets say the distance you are travelling is 40 miles.
The first 20 miles takes you one hour to do.
To average 40 miles an hour, you would have to travel 40 miles in one hour, or 80 miles in two, but you only have 40 miles total to go at, and you've already used your hour up, so you would have to do the second half in zero time.
Same works for all other distances....
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What Johnny is saying is that if you travel half way at 20mph, it is impossible to double the average mph as the second leg would have to be done in zero time,
Example: you have a journey of 80 miles. If you travel the first 40miles at 20mph it will take you 2hours. You are still only half way there. You still need to do the other 40miles.
For an average speed of 40mph you need to do the 80miles in 2hours.
Example: you have a journey of 80 miles. If you travel the first 40miles at 20mph it will take you 2hours. You are still only half way there. You still need to do the other 40miles.
For an average speed of 40mph you need to do the 80miles in 2hours.
oilman said:
How does 'average' work: you're aim is 40mph, the one known unit is 20, you need to know the second unit.
40 times two units = 80. The known unit is 20, so 80 minus 20 = 60
Same answer as crafty.
How do you get to the 30?
Now Esso, Asda and Tesco have dropped their prices I bet those silly sod's that kept brimming their tanks with more expensive fuel over the last week for the "shortage" feel stupid now. My tank is nearly empty!!! Just enough to get to the local Tesco (I hope!!!)
Say distance is 60 miles. Do the first 30 miles at 30mph. That takes 1 hour. So you have 1/2 hr left to do the next 30, so you need to go at 60. Average =40
The average you are looking for is SPEED. If you did the first 1/2 of the TIME at 20, and the next 1/2 of the TIME at 60 you would average 40. The problem is, doing the first 1/2 of the DISTANCE at 20 uses all the time you had if you want to average 40.
You always have to cover half the distance at more than 1/2 the average speed to stand any chance of achieving the average speed for the whole distance.
The average you are looking for is SPEED. If you did the first 1/2 of the TIME at 20, and the next 1/2 of the TIME at 60 you would average 40. The problem is, doing the first 1/2 of the DISTANCE at 20 uses all the time you had if you want to average 40.
You always have to cover half the distance at more than 1/2 the average speed to stand any chance of achieving the average speed for the whole distance.
oilman said:
Yes, correct IF you are restricting the drive TIME, but that was not the original question. You're adding a third (known) unit.
Alright then why not pick some other distances? I am not restricting the drive time, this is set by the distance and the average speed required of 40mph. We'll have 200 miles as no one has picked that yet.
100 miles at 30 mph takes 200 minutes. 100miles at 60 mph takes 100 minutes. Total 300 mins.
200 miles at 40 mph takes 5 hours. 5 hours x 60 mins = ..........?
Work it out for any other numbers. You don't have to use 30 and 60, BUT if you use 20 all your time will be taken doing the first half distance.
You could do it at 21mph for the first half, that will take 4.7619 hours, giving you just under 1/4 hour do do the next 100 miles, so if you get a move on at 420 mph you will have 0.6 milliseconds or so to spare for a comfort break.
100 miles at 30 mph takes 200 minutes. 100miles at 60 mph takes 100 minutes. Total 300 mins.
200 miles at 40 mph takes 5 hours. 5 hours x 60 mins = ..........?
Work it out for any other numbers. You don't have to use 30 and 60, BUT if you use 20 all your time will be taken doing the first half distance.
You could do it at 21mph for the first half, that will take 4.7619 hours, giving you just under 1/4 hour do do the next 100 miles, so if you get a move on at 420 mph you will have 0.6 milliseconds or so to spare for a comfort break.
Oilman, I stand corrected.
Not because of your answer, which made me think again of course.
No, because based on the original question, the only correct answer is given by johnny-t.
Example: your journey is 100 miles and you're planned average speed is 40 mph. After halve the distance at 20 mph you want to increase your speed to still get this average.
100 miles at 40 mph = 2.5 hours
half the distance (50 miles) at 20 mph takes you 2.5 hours.
Well spotted johnny-t (I will order a warp-drive next)
Not because of your answer, which made me think again of course.
No, because based on the original question, the only correct answer is given by johnny-t.
Example: your journey is 100 miles and you're planned average speed is 40 mph. After halve the distance at 20 mph you want to increase your speed to still get this average.
100 miles at 40 mph = 2.5 hours
half the distance (50 miles) at 20 mph takes you 2.5 hours.
Well spotted johnny-t (I will order a warp-drive next)
I wasn't trying to give "the only correct answer" as johnny-t and Spark123had already done that, I was trying to give examples so people could picture what was happening, as they seem to be mixing (speed x time) and (speed x distance).
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