Lesson Flying back and forth

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<H2>Flying back and forth</H2>

<H3>Problem 1</H3>Joe and &nbsp;Frank want to meet each other half way between their cities. 
The distance between their towns is &nbsp;36 &nbsp;miles. 
Both travel at &nbsp;6 &nbsp;miles per hour. &nbsp;Joe takes a carrier pigeon and sets it off toward &nbsp;Frank. 
The pigeon travels at &nbsp;18 &nbsp;miles an hour. &nbsp;When it reaches &nbsp;Frank it turns around immediately and returns to &nbsp;Joe. 
What is the distance the pigeon covers when the two friends meet? &nbsp;The pigeon does not take a rest.

<B>Solution</B>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is well known &nbsp;{{{highlight(highlight(CLASSIC))}}} &nbsp;entertainment problem.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Its standard solution is in &nbsp;3 &nbsp;lines.

<pre>
Joe and Frank approach each other at the rate 6+6 = 12 miles per hour.

Hence, they will meet each other in 36/12 = 3 hours.

During these 3 hours, flying at the rate of 18 miles per hour, the pigeon will cover the distance of 3*18 = 54 miles.   <U>ANSWER</U>
</pre>

<H3>Problem 2</H3>Two bees leave simultaneously two locations &nbsp;150 &nbsp;meters apart and fly, &nbsp;without stopping, 
back and forth between these two locations at average speeds of &nbsp;3 &nbsp;meters per second 
and &nbsp;5 &nbsp;meters per second, &nbsp;respectively. 
&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;&nbsp;How long is it until the bees meet for the first time? 
&nbsp;&nbsp;&nbsp;&nbsp;(b) &nbsp;&nbsp;How long is it until they meet for the second time?

<B>Solution</B>

<pre> 
(a)  Question (a) is simple. Initial distance is 150 meters and the rate of approaching is

3 + 5 = 8 m/s.  So, the time till the first meeting is  150/8 = 18.75 seconds.    <U>ANSWER</U>

At this point, part (a) is complete.

(b)  Faster bee covers 150 m in  150/5 = 30 seconds, and after that changes the direction to opposite.

Slover bee covers 150 m in  150/3 = 50 seconds.

So, when the faster bee completes 150 m in 30 seconds, the slower bee is still on the way to its turning point,

and the slower bee will fly additional 50-30 = 20 seconds to get its turning point.

During these 20 seconds, the faster bee, which just changed its direction to opposite,
     will cover 20*5 = 100 meters.

So, when the slower bee will reach its turning point, the distance between the bees will be 150 - 100 = 50 m.

Now both bees fly towards each other at the approaching rate of 3+5 = 8 m/s (again).

So, they will cover  50 m  in 50/8 = 6.25 seconds.

Thus, the time to meet for the second time is 30 + 20 + 6.25 = 56.25 seconds (counting from the start).    <U>ANSWER</U>

It is the same as to say that they will meet in the second time 56.25 - 18.75 = 37.5 seconds after their first meeting moment.
</pre>

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