Question 1206959
<pre>
To make the fractions easy to use, suppose the tank holds 35 gallons, or
35 of any unit of volume you choose.

At 2:30, the tank contains 21 gallons. (3/5 of 35)
55 minutes later (at 3:25) the tank contains 10 gallons. (2/7 of 35).

So it leaked out 11 gallons in 55 minutes. (21-10)
How long will it take to leak out those remaining 10 gallons?

Set up the proportion: (gallons over minutes equals gallons over minutes):

{{{matrix(1,2,11,gallons)/matrix(1,2,55,minutes)}}}{{{""=""}}}{{{matrix(1,2,10,gallons)/matrix(1,2,x,minutes)}}}

{{{11x}}}{{{""=""}}}{{{550}}}

{{{x}}}{{{""=""}}}{{{50}}}

So 50 minutes after 3:25 is 4:15. 

----------------------------------------

Here's an alternate way to get the answer without changing any of the
original information (not the easiest way! LOL)

Let x = the number of hours after 12 noon or midnight
Let y = the fraction of fullness the tank is at time x.

We want to know what x is when y = 0.

When its {{{2&30/60}}} hours past 12 noon or midnight, it's {{{3/5}}}ths full.
When its {{{3&25/60}}} hours past 12 noon or midnight, it's {{{2/7}}}ths full.

So we want the equation of the line through the points:

{{{(matrix(1,3,2&30/60,",",3/5))}}} and {{{(matrix(1,3,3&25/60,",",2/7))}}}
which is
{{{(matrix(1,3,2&1/2,",",3/5))}}} and {{{(matrix(1,3,3&5/12,",",2/7))}}}
which is
{{{(matrix(1,3,5/2,",",3/5))}}} and {{{(matrix(1,3,41/12,",",2/7))}}}

Slope formula:
{{{m}}}{{{""=""}}}{{{(y[2]-y[1])/(x[2]-x[1])}}}
where (x<sub>1</sub>,y<sub>1</sub>) = {{{(matrix(1,3,5/2,",",3/5))}}}
and where (x<sub>2</sub>,y<sub>2</sub>) = {{{(matrix(1,3,41/12,",",2/7))}}}

{{{m}}}{{{""=""}}}{{{(2/7-3/5)/(41/12-5/2)}}}
Multiply top and bottom by {{{12*7*5=420}}}

{{{m}}}{{{""=""}}}{{{(120-252)/(1435-1050)}}}{{{""=""}}}{{{(-132)/385)}}}{{{""=""}}}{{{-12/35}}}

Point-slope formula:
{{{y-y[1]}}}{{{""=""}}}{{{m(x-x[1])}}}
where (x<sub>1</sub>,y<sub>1</sub>) = {{{""=""}}}{{{(matrix(1,3,5/2,",",3/5))}}}
{{{y-3/5}}}{{{""=""}}}{{{expr(-12/35)(x-5/2)}}}

Substituting 0 for y, to find when tank is empty:

{{{-3/5}}}{{{""=""}}}{{{expr(-12/35)(x-5/2)}}}

Multiply through by 35
{{{-21}}}{{{""=""}}}{{{-12(x-5/2)}}}

{{{-21}}}{{{""=""}}}{{{-12x+30)}}}

{{{-51}}}{{{""=""}}}{{{-12x)}}}

{{{(-51)/(-12)}}}{{{""=""}}}{{{x}}}

{{{17/4}}}{{{""=""}}}{{{x}}}

{{{4&1/4}}}{{{""=""}}}{{{x}}}

So the tank became empty at 4 1/4 hours after 12 noon or midnight.

1/4 of an hour is 15 minutes

So the instant the tank became empty was at 4:15 PM or AM

Edwin</pre>