Question 338228
1. if it takes john 900 seconds to run 1 mile then he is running at a rate of 4 mph.
show work
<pre><b>
{{{1mi/900sec}}}{{{"×"}}}{{{(60sec)/(1min)}}}{{{"×"}}}{{{(60min)/(1hr)}}}

Cancel the seconds:

{{{1mi/900cross(sec)}}}{{{"×"}}}{{{(60cross(sec))/(1min)}}}{{{"×"}}}{{{(60min)/(1hr)}}}

Cancel the minutes:

{{{1mi/900cross(sec)}}}{{{"×"}}}{{{(60cross(sec))/(1cross(min))}}}{{{"×"}}}{{{(60cross(min))/(1hr)}}}

All that's left is

{{{(mi*60*60)/(900hr)}}}

{{{(3600mi)/(900hr)}}}

{{{4mi/hr}}}

{{{4expr(mi/hr)}}}
</pre></b>
2. Three consecutive odd counting numbers have the property that the sum of the largest and twice the smallest is 64. what is the middle number.
<pre><b>
Smallest of the three consecutive odd integers = n
Middle of the three consecutive odd integers = (n+2)
Largest of the three consecutive odd integers = (n+4)

largest + 2*smallest = 64

         (n+4) + 2*n = 64

         n + 4 + 2n  = 64

              3n + 4 = 64

                  3n = 60

                   n = 20

But 20 is even, not odd.  If the problem had asked for three consecutive
even counting numbers, they would be

Smallest = n = 20
Middle = (n+2) = 20+2 = 22
Largest = (n+4) = 20+4 = 24

The largest, 24 plus twice the smallest, 2*20 or 40, is 64, since 24+40 = 64.
But they're even, not odd.

Thus, there is no solution, since they must be odd.  Only such even
consecutive counting numbers exist, but no odd ones. 

Edwin</pre>