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April 26th, 2018, 01:06 PM  #1 
Newbie Joined: Apr 2018 From: Braintree MA Posts: 7 Thanks: 0  Normalizing units
Hi, This is probably very easy but it is escaping me. Have not been in a math class in 28 years. Please help me to solve the following problem. .748 gallons per 89 Seconds = X gallons per minute. I can figure it out using commons sense, but I am looking for a methodical approach. I assume my first step would be to get rid of Seconds and only work with minutes. I know there is 60 seconds in a minute, but again, I am looking for a methodical approach. How would I write the equation? I think I will have to use cross multiplication and possible reciprocals. Please forgive the cobwebs in my head, this stuff used to be second nature to me. I imagine the equation would start off like this? .78 Gallons / 89 seconds = X Gallons / Minute Thank you! Last edited by snewonoj; April 26th, 2018 at 01:11 PM. Reason: Started an equation to communicate my thought process. 
April 26th, 2018, 01:22 PM  #2  
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468  Quote:
 
April 27th, 2018, 04:44 AM  #3 
Newbie Joined: Apr 2018 From: Braintree MA Posts: 7 Thanks: 0 
JeffM1, You hit the nail on the head recommending this video. Refreshes my memory in a big way! I forgot how much fun math really is. "Dimensional Analysis" was such a foundational skill in my early profession that I remembered enough to ask the right questions, but was frustrated that I could not organize my thoughts. This video really helps. Grateful, Jonathan 
April 27th, 2018, 05:20 AM  #4 
Newbie Joined: Apr 2018 From: Braintree MA Posts: 7 Thanks: 0 
So Dimensional analysis is definitely helpful to get me to this point. .748 gallons / 89 seconds is the same as .748 gallons / 1.48 minutes. So how do I solve for how many gallons per minute? I know that to go from 1.48 minutes to 1 minute I would multiply it by .675675676, so should I multiply both the .748 gallons and the 1.48 minutes by .675675675? What would that look like in an equation? Thank you. Last edited by skipjack; April 27th, 2018 at 07:06 AM. 
April 27th, 2018, 05:41 AM  #5 
Newbie Joined: Apr 2018 From: Braintree MA Posts: 7 Thanks: 0 
I think I got it. .748 Gallons / 1.48 minutes is the same as .505405 gallons per minute. The equation looks like: .748 gallons / 1.48 minutes = X / 1 minute cross multiply to get .748 gallons = 1.48 X divide both sides by 1.48 to solve for x The part that has me so confused is I do not know when to drop Gallons or Minutes from the equation. Neither cancel out, so why isn't 1.48X shown as 1.48 Gallons/minute X ? Thank you, Jonathan 
April 27th, 2018, 06:39 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468 
I must admit that I tend to think about dimensional analysis as an algorithm rather than as an equation, probably because when I learned it I was doing so to figure out how to get a numeric answer on a slide rule. So let's start that way. I have a rate expressed in terms of a certain number of gallons per a certain number of seconds. I want to convert it to use minutes rather than seconds. Per means that seconds is in the denominator so to cancel that unit the conversion factor must have seconds in the numerator. $\dfrac{0.748\ gallons}{89\ seconds} * \dfrac{60\ seconds}{1\ minute} = \dfrac{0.748 * 60 \ gallons}{89 \ minutes} = \dfrac{0.748 * 60}{89}\ gallons \ per \ minute.$ Now just haul out your slide rule or hand calculator. But of course you can think of it as solving an equation for a number x. Numbers do not have dimensions. $\dfrac{0.748\ gallons}{89 \ seconds} = x * \dfrac{1\ gallon}{1\ minute} \implies x = \dfrac{0.748 * 1 \ gallon * minutes}{89 \ gallon * seconds} \implies$ $x = \dfrac{0.748 \ minutes}{89 seconds} * 1 = \dfrac{0.748 \ minutes}{89 \ seconds} * \dfrac{60\ seconds}{1\ minute} = \dfrac{0.748 * 60}{89}.$ Same result, different thought process. You may ask where did $1 = \dfrac{60\ seconds}{1\ minute}$ come from? $60\ seconds = 1 \ minute \implies \dfrac{60\ seconds}{1\ minute} = 1.$ 
April 27th, 2018, 07:24 AM  #7  
Global Moderator Joined: Dec 2006 Posts: 19,542 Thanks: 1751  Quote:
As 89/60 isn't exactly 1.48, calculate .748/(89/60) as 0.5042..., i.e. 0.504 after rounding to three significant figures.  

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