Monday, March 5, 2012

The Solution to the Interstate 80 Problem

Okay Puzzlers, the key to this problem is the old formula: Distance = Rate X Time or D = RT

Now on my atlas the distance on I-80 from San Francisco to New York is 2944 miles.  We also know that the motorcycle traveled at 65 mph and the Mustang went 85 mph.

Using D = RT we get:

Motorcycle:  D = 65T         Mustang:  D = 85(T-1) because the Mustang left an hour later.

These two distances span the nation, so adding them we get the equation:

65T + 85(T-1) = 2944, okay then let's solve.

65T + 85T - 85 = 2944 distributing 85 across the parenthesis

150T - 85 = 2944 adding the variable terms

150T = 3029 adding 85 to both sides of the equation.

T = 20.19 dividing both sides by 150

20.19 hours is about 20 hours and 11.4 minutes, so the time would be about 8:11 the next morning.  It is the same for the Mustang.  He leaves an hour later but travels only 19.19 hours arriving at the same time.

This translates into the following miles for each vehicle:

Motorcycle - 1312.35 miles    Mustang - 1631.15 miles, fortunately these add up to basically 2944 miles

Working across the nation on my atlas I came up with about 48 or 49 miles east of Omaha, the closest town there was a place called Waverly, NB.

I hope you enjoyed this as much as I did.  If you disagree or just generally feel I have my head up my rear end, feel free to leave me a comment.

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