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Chapter 2: Problem 5

A hospital patient is given 500 cc of saline by IV. If the saline is received at a rate of \(4.0 \mathrm{~mL} / \mathrm{min},\) how long will it take for the half liter to run out?

Short Answer

Expert verified
It will take 125 minutes.

Step by step solution

01

Convert Units

First, we need to recognize that 500 cc is equivalent to 500 mL because 1 cc is the same as 1 mL. Hence, the total volume is 500 mL.
02

Use the Rate Formula

The formula we use here is the time formula, which is \[ \text{Time} = \frac{\text{Volume}}{\text{Rate}} \]where the volume is 500 mL, and the rate is 4.0 mL/min.
03

Perform the Calculation

Substitute the known values into the formula:\[ \text{Time} = \frac{500 \text{ mL}}{4.0 \text{ mL/min}} = 125 \text{ minutes} \]This calculation divides the total volume (in mL) by the rate (in mL/min) to get the total time in minutes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit Conversion
Unit conversion is the process of converting a measurement from one unit to another. It is essential for solving problems where measurements are presented in different units. For example, in the medical field, volumes are often measured in both cubic centimeters (cc) and milliliters (mL). Luckily, converting between these two units is straightforward:
  • 1 cc is exactly equivalent to 1 mL.
To convert 500 cc to mL, you simply need to recognize that the numerical value stays the same, resulting in 500 mL. This conversion is crucial for aligning units, which ensures consistency when applying formulas. Always make sure that all measurements are in the same unit before performing calculations.
Volume Calculation
Volume calculation involves determining the amount of space occupied within a container or object. In this exercise, the volume of the saline solution is given as 500 cc, which we converted to 500 mL.
Volume is an important parameter in calculation problems, especially in contexts like medicine where precise dosages are critical. Whenever you're working with problems involving liquids, make sure to understand the volume that needs to be administered or analyzed.
Remember:
  • Keep track of the volume units used.
  • Convert to a consistent unit if necessary.
This understanding allows for accurate calculations involving flow rates and dosage times.
Rate Formula
The rate formula helps determine how long it takes to complete a process when a certain flow rate is involved. It's a critical tool in calculations where something happens over time, such as administering saline through an IV.
The general formula is: \[\text{Time} = \frac{\text{Volume}}{\text{Rate}}\]This formula calculates time by dividing the total volume by the rate at which the volume decreases. In our saline example:
  • The total volume is 500 mL.
  • The rate is 4.0 mL/min.
Substitute these into the formula to obtain the time required for the process. This formula is invaluable in fields requiring precise timing and delivery of substances, ensuring a controlled and measured approach.
Time Calculation
Time calculation involves determining the duration required to complete a task. Once you've set up your units and known values using the rate formula, the next step is simply calculating the time.
By substituting known values into the formula \(\text{Time} = \frac{500 \text{ mL}}{4.0 \text{ mL/min}}\), you get:
  • \(\text{Time} = 125 \text{ minutes}\)
This value tells you how long it will take for the IV saline to be fully administered. Breaking down the calculation into simple arithmetic helps ensure accuracy. Make sure to double-check units and calculations, especially in real-world applications where timing can be critical.

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Most popular questions from this chapter

In an air bag test, a car traveling at \(100 \mathrm{~km} / \mathrm{h}\) is remotely driven into a brick wall. Suppose an identical car is dropped onto a hard surface. From what height would the car have to be dropped to have the same impact as that with the brick wall?

After landing, a jetliner on a straight runway taxis to a stop at an average velocity of \(-35.0 \mathrm{~km} / \mathrm{h}\). If the plane takes \(7.00 \mathrm{~s}\) to come to rest, what are the plane's initial velocity and acceleration?

A sports car can accelerate from 0 to \(60 \mathrm{mi} / \mathrm{h}\) in \(3.9 \mathrm{~s}\). What is the magnitude of the average acceleration of the car in meters per second squared?

IE oo A race car travels a complete lap on a circular track of radius \(500 \mathrm{~m}\) in \(50 \mathrm{~s}\). (a) The average velocity of the race car is (1) zero, (2) \(100 \mathrm{~m} / \mathrm{s},\) (3) \(200 \mathrm{~m} / \mathrm{s},\) (4) none of the preceding. Why? (b) What is the average speed of the race car?

An object moves in the \(+x\) -direction at a speed of \(40 \mathrm{~m} / \mathrm{s}\). As it passes through the origin, it starts to experience a constant acceleration of \(3.5 \mathrm{~m} / \mathrm{s}^{2}\) in the \(-x\) -direction. (a) What will happen next? (1) The object will reverse its direction of travel at the origin; (2) the object will keep traveling in the \(+x\) -direction; (3) the object will travel in the \(+x\) -direction and then reverses its direction. Why? (b) How much time elapses before the object returns to the origin? (c) What is the velocity of the object when it returns to the origin?
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