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Our story takes place in the future. Earth has been invaded by an evil alien species, known by the humans as simply, "The Bots". They are essentially robots, but sophisticated and evil. Humans have also evolved, being bigger, stronger, and faster.

The Bot Viri's radar picked up the human Mr. Johnson at the same time that Johnson, who had been hunting in the forest (food has been scarce since the invasion), became aware of loud electrical noises emitting from the direction of the Bots mountain headquarters.

Chase

Johnson realized the bot was active and might try to catch him. Knowing that Bots are "afraid of water" because it will short-circuit them, he began to run toward the seashore.

Bot Viri locked-on to Johnson's position but hesitated for 6 seconds before he began to run after Johnson.

Bot Viri was 5 miles directly north of Johnson when Johnson began to run toward the sea 2 miles directly to his south.

Johnson, who could run much faster than humans of the past, ran at a rate of 20 miles per hour over the 2-mile distance. Viri's speed, though, was not constant. He ran the first mile at a rate of 20 mph, the second mile at a rate of 40 mph, the third at a rate of 80 mph, the fourth at a rate of 160 mph, and so forth—doubling his speed after running each mile.

An acceptable solution will answer the following questions:

Did Johnson make it to the safety of the sea?

Flowchart

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  • $\begingroup$ I feel like this is more of a textbook maths question than a puzzle. If you take away all the pictures and context, which aren't actually needed, it's just a simple maths problem. $\endgroup$ – Beastly Gerbil Apr 11 '20 at 20:52
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    $\begingroup$ There are thousands of great puzzles on here that are based on mathematics. As far as being "simple math" , well that is wonderful for new students or people just learning. We have to remember, 'simple' is relative. This puzzle may not be as easy to solve for some. Either way, we post puzzles to encourage and promote mathematics. This site is a blessing in that respect - it makes learning FUN by wrapping boring math in riddles and puzzles. :) $\endgroup$ – John S. Apr 11 '20 at 21:07
  • $\begingroup$ I understand what you are saying, but you have to be 13+ to sign up here, and simple maths puzzles usually get closed, as they belong on math.stackexchange.com instead. If it wasn't for all the flavour here I would be voting to close. And even then I'm unsure, because the flavour is completely unneeded and this is a simple maths problem when you look at the actual question here. $\endgroup$ – Beastly Gerbil Apr 11 '20 at 21:37
  • $\begingroup$ The last thing we want to do here is to post anything not deemed as useful. If you want to close this puzzle, we will try to make another one more challenging. $\endgroup$ – John S. Apr 11 '20 at 21:55
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Did Viri catch Johnson?

No

And the follow on questions...

How many did Johnson have to spare? 3.1875s. J ran 20mph, which means he covered his distance of 2 miles in 6 min.
V had 7 miles to cover (5 miles to reach J’s original position + 2 miles). V’s rate of travel. Mile 1 | 20mph | 3 min. Mile 2 | 40mph | 1.5 min. Mile 3 | 80mph | 0.75 min. Mile 4 | 160mph| 0.375 min. Mile 5 | 320mph| 0.1875 min.
Mile 6 | 640mph| 0.09375 min. Mile 7 | 1280mph| 0.046875 min. V’s final speed was 1280mph V’s Total travel time was 5 min and 57.1875 seconds. BUT.... Viri hesitated 6 seconds before starting so arrived at the coast 6 min and 3.1875s after J started running.
J had 3.1875s to enjoy his swim before V arrived.
He who hesitates is lost, Viri.

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