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Sarah Lee was late for work. Again. This time it was no joke. She quickly got into her car, and saw that it was nearly out of gas. But there was no time to fill up. "Fastest route will be 24 miles and 35 minutes," the GPS told her. Sarah saw that she only had 14 miles left on her car before she would be stuck. She presses the button on the GPS.

Recalculating...

How can Sarah get to work without running out of gas?

For those who wanted clarification:
Sarah Lee works in a physical building located some distance from her house.
Sarah Lee needs to drive her car from her house to her place of work.
Sarah Lee needs to get to work without running out of gas.
Sarah Lee has no time to get more gas for her car before work.
Sarah Lee can driver her car for 14 miles before running out of gas.

Hint:

How do GPSs calculate routes?

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  • $\begingroup$ Does she have to get to work via car, and is the shortest distance between her initial point and work greater than 14 miles? $\endgroup$ – HDE 226868 Mar 4 '16 at 0:41
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    $\begingroup$ Too broad? ...a slower route could still be shorter (14mi), could be rolling downhill, her job could be remote/mobile meaning it can come to her, she could take a cab/bike/run/hitch/etc instead, maybe she drives the 14 miles really fast and then walks the rest, maybe she works for the GPS company and knows her product is rubbish and it's actually only 14 miles, maybe her GPS system works in base5 and 24 miles is actually only 14 (base10) miles.... $\endgroup$ – Alconja Mar 4 '16 at 1:21
  • $\begingroup$ I'm going with too broad unless OP adds in additional details $\endgroup$ – LinkBerest Mar 4 '16 at 2:10
  • $\begingroup$ @JGreenwell how about now? $\endgroup$ – LN6595 Mar 6 '16 at 18:52
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    $\begingroup$ I would be interested to see what answer OP was looking for. $\endgroup$ – Trenin Mar 7 '16 at 12:56
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The fastest route is 24 miles, but the shortest route is 14 or less.

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Sarah Lee...

should tailgate the **** out of a truck.

Tests proved that driving 10 feet behind a truck could result in a 45% gas usage reduction (source).

Which means that the 14 miles she could usually drive are divided by 0.55 times her usual gas mileage => 14 / 0.55 = 25.45 miles.

That distance being longer than the 24 miles she needs to drive on the fastest route, she'll hopefully make it alive and on time!!! :D

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  • $\begingroup$ This is both illegal and dangerous, but I guess that's lateral thinking for you. $\endgroup$ – Joe Z. Mar 7 '16 at 22:25
  • $\begingroup$ Yeah guys, don't do this. $\endgroup$ – phenxd Mar 8 '16 at 2:26
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Sarah Lee...

has an amphibious vehicle.

Her GPS is incorrect because...

It's not taking bodies of water into account. She can easily avoid the long drive around by simply driving straight into the water and boating across.

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Maybe her work was down a hill that was ten miles long that was 14 mile away and she could just coast down the hill for the last 10 miles.

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She drives across the field that she would normally drive around. Because $14^2 + 14^2 < 24^2$, it's possible there is some non-road surface separating her from work.

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