First rate: $\\var{r1}\\,\\text{mL/hr}\\times \\var{delay}\\,\\text{hr}=\\var{r1*delay}\\,\\text{mL}$
\nAfter that time the patient will still require $\\var{V}\\,\\text{mL}-\\var{r1*delay}\\,\\text{mL}=\\var{vleft}\\,\\text{mL}$.
\nSecond rate:
\n\\begin{align}\\text{time (hr)}&=\\frac{\\text{volume (mL)}}{\\text{flow rate (mL/hr)}}\\\\&=\\frac{\\var{Vleft}\\text{ mL}}{\\var{r2} \\text{ mL/hr}}\\\\&=\\var{secondhour} \\text{ hours and } 0 \\text{ minutes} \\end{align}
\nTotal time: $\\var{delay}\\,\\text{hr}+\\var{secondhour}\\,\\text{hr}=\\var{h}\\text{ hr}.$
\n\\begin{align}\\text{time (hr)}&=\\frac{\\text{volume (mL)}}{\\text{flow rate (mL/hr)}}\\\\&=\\frac{\\var{Vleft}\\text{ mL}}{\\var{r2} \\text{ mL/hr}}\\\\&\\approx \\var{time-delay} \\text{ hours} \\\\&=\\var{secondhour} \\text{ hours and } \\var{m} \\text{ minutes}\\end{align}
\nTotal time: $\\var{delay}\\,\\text{hr}+\\var{secondhour}\\,\\text{hr}+\\var{m}\\, \\text{min}=\\var{h}\\text{ hours and } \\var{m} \\text{ minutes}.$
\n\\begin{align}\\text{time (hr)}&=\\frac{\\text{volume (mL)}}{\\text{flow rate (mL/hr)}}\\\\&=\\frac{\\var{Vleft}\\text{ mL}}{\\var{r2} \\text{ mL/hr}}\\\\&= \\var{time-delay} \\text{ hours} \\\\&=\\var{secondhour} \\text{ hours and } \\var{m} \\text{ minutes}\\end{align}
\nTotal time: $\\var{delay}\\,\\text{hr}+\\var{secondhour}\\,\\text{hr}+\\var{m}\\, \\text{min}=\\var{h}\\text{ hours and } \\var{m} \\text{ minutes}.$
\n", "variables": {"time": {"definition": "h+m/60", "description": "", "name": "time", "group": "Ungrouped variables", "templateType": "anything"}, "type": {"definition": "random(1,2,3,4)", "description": "", "name": "type", "group": "Ungrouped variables", "templateType": "anything"}, "vleft": {"definition": "V-r1*delay", "description": "", "name": "vleft", "group": "Ungrouped variables", "templateType": "anything"}, "delay": {"definition": "random(1..4)", "description": "", "name": "delay", "group": "Ungrouped variables", "templateType": "anything"}, "secondhour": {"definition": "random(1..4)", "description": "", "name": "secondhour", "group": "Ungrouped variables", "templateType": "anything"}, "r2": {"definition": "random(50..400#25)*type", "description": "", "name": "r2", "group": "Ungrouped variables", "templateType": "anything"}, "h": {"definition": "delay+secondhour", "description": "", "name": "h", "group": "Ungrouped variables", "templateType": "anything"}, "m": {"definition": "switch(type=1,0,type=2,random(0,30),type=3,random(20,40), type=4,random(15,30,45))\n", "description": "", "name": "m", "group": "Ungrouped variables", "templateType": "anything"}, "V": {"definition": "r1*delay+r2*(secondhour+m/60)\n", "description": "", "name": "V", "group": "Ungrouped variables", "templateType": "anything"}, "r1": {"definition": "random(50..400#25 except r2)", "description": "", "name": "r1", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "customName": "", "scripts": {}, "marks": 0, "unitTests": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "gaps": [{"correctAnswerFraction": false, "precisionPartialCredit": 0, "useCustomName": false, "minValue": "h", "allowFractions": false, "precisionType": "dp", "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "precision": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the nearest whole number.", "customMarkingAlgorithm": "", "scripts": {}, "marks": 1, "mustBeReducedPC": 0, "type": "numberentry", "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "maxValue": "h"}, {"correctAnswerFraction": false, "useCustomName": false, "minValue": "m", "allowFractions": false, "variableReplacements": [], "showFractionHint": true, "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "scripts": {}, "marks": 1, "mustBeReducedPC": 0, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "adaptiveMarkingPenalty": 0, "maxValue": "m"}], "showCorrectAnswer": true, "sortAnswers": false, "prompt": "Your patient is ordered $\\var{V}$ mL of a fluid. If the IV is set at $\\var{r1}$ mL/hr, and then after $\\var{delay}$ hours the rate is changed to $\\var{r2}$ mL/hr, how long will the total infusion take?
\n[[0]] hours [[1]] minutes
"}], "metadata": {"description": "Nursing question. IV question. Given volume required, the rate for some hours and then another rate afterwards, how long will it take to get the required volume? Answers are designed to be easy to handle, e.g. full hours, half hours, quarter hours and thirds of an hour.", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "tags": [], "name": "IV time needed with a rate change (easier)", "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "Evaluate the following without using a calculator.
\nIf you are unsure of how to do a question, click on Reveal answers to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.
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