How Fast Was The Bus Going?

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Here is a puzzler for you math-oriented aspies.

I was driving home this afternoon from a road trip. I was headed north on interstate 95 in central Maine. I came around a corner and there was a Greyhound bus (about, but lets say) exactly one mile ahead of me. I was at mile marker 140 and this bus was one mile ahead of me. My cruise control was set at 73 miles per hour and I did not accelerate or slow down during this part of the trip, also assume the bus had cruise control set on his particular speed. By the time I reached mile marker 163 the bus was (again, approximately but lets say) exactly one mile behind me.

How fast was the bus going?

I'm going to hazard a guess at 66.65mph just completely randomly. No calculations or anything. Well, a few.

Not a puzzler though.

Last edited by MisterSpock on 19 Nov 2012, 1:36 pm, edited 1 time in total.

I suck at math but I can deduce the following:

Interstates have no corners

In 23 miles you only gained 2 miles on the bus

Diesel engines are governed to a peak engine RPM for the most part. Given the acceleration characteristics the engine acts as its own cruise control.

Going up a hill the bus would naturally slow down, especially in light of the taller gearing provided by the larger diameter wheels

Dashboard speedometers are all calibrated to read higher than actual speed.

You say "by the time" you reached Marker B, but leave out how many minutes actually passed since Marker A. Realistically you could have both been going 58-63 before the bus lost momentum going uphill

App. 65.63 mph, assuming that the bus was indeed on cruise control.

Calculation

You were going 73 mph over a distance of 23 miles.

d/t = v
23/t = 73
t = 23/73 = 0.32

The bus covered a distance of 21 miles in the same time

21/0.32 = 65.63

Nice.

Simple really. It took you twenty three miles to gain two miles on the bus. (The one mile you were behind plus the one mile you ended up ahead). If you had only gained one mile on the bus (caught up to it), the relative difference in your speed would have been exactly twenty three miles per hour. Since you gained double that, the relative speed differential is only half that, or 11.5 mph. 73 - 11.5 = 61.5 (Of course this is assuming your approximations are accurate, and the speeds are averages.)

New Dawn already got it, but you did assume more information than necessary:
(and my special interest is buses)

-Yes the engine is governed, on this model the governor is 73mph, it could go the same speed i was going

-The stretch was more or less flat. Also, the bus was at a speed below governor, therefore could maintain a speed on a reasonable grade

-Assume my speedo and the bus speedo were both calibrated to the exact MPH

-You could easily have figured out how much time it took both of us to travel the distance. 23/73=0.31 hours= 18.9 minutes

Did I not, given reasonable rounding error? I was only ~0.03% different from New Dawn

New Dawn showed their work Your answer was reasonable however.

My mind has totally shut down. I must be terrible at maths!

Explanation of the equation I used starts at 5:25 to 6:55

[youtube]http://www.youtube.com/watch?v=8Ig-e509uRQ[/youtube]

Did it again. Of course you DO realize this is going to bug me until I figure out exactly WHAT I did wrong. You people are evil. EVIL I tell you!

No, don't tell me. I want to figure it out MYSELF. Pthpthpth!

I don't mean to be all litteral n' s**t but I think spock's answer was more than reasonable considering it is closer to the true value based on your parameters. Absolutely nothing against dawn because rounding is totally acceptable in most real world situations but the rounding (.32) threw the answer off slightly. New dawn showed his/her work but spock was closer to the true answer. In fairness you specifically asked for the answer, not the work to show how it was done, and spock came closer to answering the question. I still don't know why people are more interested in showing the work than the actual solution but I know it has caused me to fail math classes despite never giving a wrong answer on the homework.

Don't look below if you still want to figure this out on your own.







































Think of it this way- The bus covers 1 mile less than the car over 11.5 miles. At 73 mph it takes the car takes ~.1575 hours to cover the 11.5 miles therefore in 1 hour the bus travels ~6.3492 miles less than the car. Since you are using mph and the bus travels ~6.3492 miles less per hour than the car. Now you know the bus is traveling 66.65 mph.

Car A starts at mile zero ( the 140 mile marker).

Car B (the bus) starts at mile one ( a mile ahead of car A).

By the time car A reaches mile 22 (the 163 mile marker), car B has reached mile 21 ( a mile behind car A final position).

In the time that car A travels 22 miles, car B travels 20 miles.

Thus Car A must be moving at a rate ten percent faster than car B.

Thus the bus (car b) is moving one eleventh, or about 9 percent slower than Car A's speed of 73mph. Or about 66.36 miles per hour.

Fast enough to get a woman pregnant.