Engineer's Puzzle

The Puzzle: Driving me MAD!

Jason Thompson, 06/06/2015
Read the question. Nobody mentioned a limit on time (ie journey had to take a total of 1 hour). It ...  Read More

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Two engineers are arguing. They'd read a puzzle in Engineering Materials magazine and were trying to convince one another that THEY were right!

The puzzle went along these lines: If you drive halfway to a town 60 miles away at a speed of 30mph (assume any time lost for acceleration or deceleration is negligible), how fast would you need to drive the rest of the way to have an average speed of 60mph over the entire trip?

You need to travel to the town directly (assume a straight line) from your half way position, and once there, you stop and turn off the engine.

Now, the two engineers 'discussing' this have very different views.

One says: "It's 90mph, you buffoon!"

While the other replies: "You idiot, it can't be done. It's impossible!"

The question is: who, if either, is right?

Solution:

On the surface an easy problem. But, it is in fact impossible.

Speed is by definition time over distance. And since the distance is fixed (30miles), and you have to go straight there, the faster you go, the less time you are travelling. Pelting it along at 90mph will get you there in 20mins. So you will cover 60miles in a total 1.33hours. So your average speed will in fact be a little over 45mph.

No matter how fast you go, you can only travel 30miles before you have to turn off the engine, and while you will get there faster, your average speed will never reach 60mph unless you instantaneously arrive from the middle point to the end point in some kind of warp hole.

Not convinced? Prove me wrong!

Justin Cunningham

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Engineer's Puzzle Entries
It is impossible to achieve this in the 30 miles remaining. In order to achieve an average speed of 60mph, you would need to travel at 90mph for an hour, and overshoot your destination by 60 miles. OK, so let's travel faster to boost our average speed. Right? Wrong! The faster you go, the quicker you will reach your destination and therefore the less time at fast speed you have to average out against your 30mph stint. Because the distance is constant at 30 miles, the distance=speed X time equation always works against you. The higher you push the speed part, the smaller the time part becomes and therefore in 30 miles you can't travel fast enough for long enough to average the first half of the journey out.

Comment Andy Lawson, 12/06/2015
Read the question. Nobody mentioned a limit on time (ie journey had to take a total of 1 hour). It can't be done legally, but it can hypothetically: you just break the speed limit and drive at 90mph for the rest of the journey. Funny thing about averages; if you calculate the remaining journey at 90mph and add the 30mph for the first half of the journey then divide the answer by two (to take the average) – wow, it works out that you will achieve an average speed of 60mph for the whole journey. Two engineers have already said something can't be done – get a grip: engineers can do anything!

Comment Jason Thompson, 06/06/2015
To average 60mph over the whole distance of 60mls., you only have a total travelling time of 1hr. As you have travelled the first half journey at 30mph., then you have already used the 1hr. allotted time. It is therefore impossible! However, on a lyrical note; If you could turn your cars mythical hyper-space drive on, and travel at a constant 96,800mph., you would reach the total 60ml. destination point, only 1.40675 seconds over the hour!

Comment Mr. Colin White., 17/03/2015
The one who said it can't be done is correct. In order to average 60 mph over 60 miles it would take 1 hour. 1 hour has already elapsed doing 30 miles at 30 mph so there is no time left.

Comment David Shawley, 17/03/2015

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