Algebra word problem help!

Question

A nurse must be careful not to inject a drug too quickly into a patient’s IV. If the drug is injected at the maximum rate of 0.075 cc per second, and the total amount to be injected is 15 cc,

a. Create an equation that tells the amount injected as a function of time (in seconds);

b. Determine the time required to complete the injection.

Answer 1

Assuming the injection rate is constant then the equation for the amount injected as a function of time is linear, i.e.

 

x = mt + b

 

where x is the amount injected, t is the time, m (the slope) is the rate, and b is the initial amount at t = 0 (which must be 0 since the injection starts at t = 0)

 

So

 

x = (0.075 cc/s)t

 

To find the time it takes to inject 15 cc set x = 15 cc and solve for t.

 

15 cc = (0.075 cc/s) t

 

t = (15 cc)/(0.075 cc/s) = 200 s.

Answer 2

Hi Kelly,

Using the equation rate x time = total.  If you let t be the time in seconds, the equation would be .075t = 15.  Dividing both sides of the equation by .075 gives you .075/.075 t = 15/.075 or t = 200 seconds.  I hope this helps.

Jody