Question 507307
A water tank is being emptied so that the height y (in feet) of the water inside the tank decreases at a linear rate with time t measured in hours past 12 noon. If the height was 15ft at 1pm and 7.5ft at 6pm, find:
:
(a)the equation relating y to t
Find the slope, assign the given values as follows
t1=1; y1=15
t2=6; y2=7.5
m = {{{(7.5-15)/(6-1)}}} = -1.5 is the slope
Use the point/slope form: y-y1 = m(x-x1), x=t
y - 15 = -1.5(t - 1)
y - 15 = -1.5t + 1.5 + 15
y = -1.5t + 16.5; is the equation
:
(b)the height at 12 noon
that occurs when t=0; 16.5 ft
:
(c)the total time required to empty the tank
That occurs when y = 0
-1.5t + 16.5 = 0
-1.5t = -16.5
t = {{{(-16.5)/(-1.5)}}}
t = +11 hrs to empty the tank