snewonoj

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!

JeffM1

Look at this youtube

snewonoj

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

snewonoj

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.

snewonoj

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

JeffM1

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?

$60\ seconds = 1 \ minute \implies \dfrac{60\ seconds}{1\ minute} = 1.$

skipjack

You lost a "4". That should be .748 Gallons / 89 seconds = X Gallons / Minute.

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.