A maths question...?

[caferacer51]

Sorry to be a pain, but I was sat at my desk all morning and couldn't work this one out, if someone could help me AND more importantly show me the calculations I'd be very greatful...

I have two choices to get to work...

1. 13.4 miles @ 39mpg (freeway/motorway) or...
2 8.6 miles @ 28mpg (30mph limit, traffic lights...)

(please take into account that this is after I've already done about 20 miles and the engine is warm etc...)

Which would use less fuel and how is that worked out?

(I'm really sorry, but I just cant work it out...)

[Hubert Farnsworth]

lets see: 13.4 mi/39mi/gal miles cancel and you're left with 0.3436 gallons used.
8.9mi/28mi/gal =0.31785 gallons used. This is only for the two effective alternate routes available after the initial 20 miles as per the problem statement.
It would appear that strictly based on distance you would come ahead even with worse mpg, however in the real world you'd need to factor in the extra time spent idling if you did not shut the engine off at the red lights, this could tip the fuel usage back into the favor of the higher speed/distance of the motor way cruise because of the higher cumulative mpg.

[bestclimb]

If you go 20 miles@ 10 mpg you burned 2 gallons
20 miles @20 mpg you burned 1 gallon
20 miles@ 40 mpg you burned .5 gallons

so miles/mpg=fuel used

13.4/39=.344 gallons
8.6/28=.307

so you save.037 gallons by going the shorter distance.

At this point I would be looking at which route took less time and was easier on me and the car. weighing how much that 0.04 gallons is worth.

[caferacer51]

aaahhhh.....

You just pointed out how many other significant variables there are in this equation...

I suppose time of day and traffic flow would factor too...?

But the figures are still relativley close, so at least I wont aggonise over which route I'd be better off taking.

Thanks for your help!