Jennifer J.

asked • 12/01/15

How will i find the ewuation that represents this situation

A hourglass is turned over with the top part filled with sand after 3 minutes there are 855 mL of sand in the top half after 10 minutes there are 750 mL of sand in the top half write a equation that represents this situation

2 Answers By Expert Tutors

By:

Andrew M. answered • 12/02/15

Tutor
New to Wyzant

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

Emiliano E. answered • 12/01/15

Tutor
5 (1)

Math Made Easy

Andrew M.

If we are looking at the flow of the sand as being
a linear equation with sand as a function of time:
We have two points (t,s) representing
ml of sand and time.  These are (3, 855) and (10, 750)
 
As Emiliano has already shown the slope of the linear equation
is found by  m=(855-750)/(10-3) = 105/7 = -15 ml/min
 
This makes sense because the sand is flowing out of the top
half at a rate of 15 ml/min thus the total amount of sand is
being reduced.
 
With the slope m = -15  we have basic equation of:
 
s = -15t + b    using the slope intercept form (y=mx+b),
or in this case  s = mt+b...
 
We can plug in either given point to find the value of b
which will give us the starting amount of sand.  Using
point (10,750) we have
 
750 = -15(10) + b
750 = -150 + b
b = 900
 
Our linear equation showing sand as a function of time is:
s(t) = -15t + 900
 
This also gives us the starting amount of sand:
At time t=0 there was 900 ml of sand in the top half of the
hourglass.
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12/02/15

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