Question

$\$3.00/\text{hour}$ is equal to how many cents/minute?

Answer 1

Hint: We are given term as 3 dollar/hour, we have t find how much it will be in cent/minute, to answer this we will first learn what is dimensional analysis than we learn how dollar is connected to cent and how the hour is connected to the minute. Then using those values we will change the dollar/hour into the cent/minute.

Complete step by step solution:
We are given 3 dollar/hour, we are asked to find how much it is in the cent/minute.
Before we start solving, we will learn that dimensional analysis is a method which helps us in converting the term from one dimension to another dimension which actually changes the value of the quantity.
For example: we know that 1 meter is the same as 100 cm, here quantity is same but dimensional are different.
So, we will first learn about how the dimensions of the dollar and cent are related and then we will learn how the hour and minutes are connected.
Now in one hour there are 60 minutes.
So, 1 hour is the same as 60 minutes.
$\Rightarrow 1\text{hour}=60\text{minutes}$ ............................ (1)
So, in each Dollar there are 100 cents it means 1 Dollar is the same as 100 cents.
$\Rightarrow 1\text{Dollar}=100\text{cent}$ ....................................... (2)
Now we use this knowledge to solve our problem.
We are given that we have 3 Dollar/hour.
$\dfrac{3\text{Dollar}}{\text{hour}}=\dfrac{3\times 1\text{Dollar}}{1\text{hour}}$
As , 1 hour = 60 minutes and
1 Dollar = 100 cent, so we get –
$\Rightarrow \dfrac{3\text{Dollar}}{\text{hour}}=\dfrac{3\times 100\text{cent}}{60\text{minutes}}$
By simplifying, we get –
$=\dfrac{3\times 10}{6}$
Simplifying further we get –
$=5\text{cent/minute}$

So, we get our solution as 5 cent/minute means 3 Dollar/hour is same as 5 cent/minute.

Note: When we have terms with multiple dimensions involved, we need to solve them separately and carefully.
If we do $\dfrac{3\text{Dollar}}{\text{hour}}$ , as just change the Dollar to cent and did not change to hour so we should not acquire the correct solution also number. If we have terms in fraction we will simplify the numerator and denominator term so that our calculation becomes easy.