
Andrew M. answered 12/02/15
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
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.
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.
Andrew M.
12/02/15