# Unit Rate Formula

## Unit Rate Definition

A rate is a ratio between two related quantities expressed as a rate of change in mathematics. If the unit or quantity in which something is changing is not given, the rate is generally expressed in terms of time.

On the other hand, a rate of change can be expressed per unit of time, length, mass, or another quantity. “Per unit of time” rates, such as speed, heart rate, and flux, are the most common types of rate. Exchange rates, literacy rates, and electric field in volts/meter are examples of non-time denominator ratios.

A unit rate is a frequent unit of measurement in our everyday lives.

Where one quantity indicates the amount of quantity contained in one unit. It doesn't matter what the quantity is. The rate is just the proportion of two quantities. When computing the unit rate, the denominator should be 1.

The unit rate formula to measure the rate for any two quantities say a and b can be given as,

Unit Rate = Ratio between two different quantities with different units

= a:b

= a/b

### Rate of Change (ROC)

The rate of change (ROC) is the speed at which a variable changes over a certain period. The rate of change (ROC) is a term that is frequently used when discussing momentum. It may be defined as a ratio between a change in one variable and a matching change in another; visually, the rate of change is represented by the slope of a line. The Greek letter delta is frequently used to represent the ROC. The unit rate of change formula is given as,

ROC =$(\frac{Current \, Value}{Previous \, Value} - 1)$ x 100

### Flow Rate Calculator

By using this calculator, it is possible to easily calculate the average volumetric flow rate of fluids by changing each of the three variables: length, pressure and bore diameter. It is also called a flow rate calculator litres per minute.

### Solved Examples

Ex.1. If a shop offers you 12 chocolates for Rs. 6.74, what has the unit cost?

Solution:

The ratio of cost per unit is

=  ${\frac{Rs.6.74}{12 \,Chocolate}}$

= 0.5616

Hence the unit cost is 0.5616

Ex.2. The bike rides at a rate of 10 miles per hour for 4 hours. Calculate rate per minute.

Solution: Given,

d = 10 miles per hours

d = 10 x 4 = 40

t = 4 hours

t = 4x60 = 240

By using the rate per unit formula we get,

Rate = d/t

Rate = 40/240

Rate = 0.1667

Hence the rate per minute is 0.1667

Ex.3. A farmer harvests 25 acres per day and gets 350 bushels of wheat per acre. Find the number of bushels of wheat he needs to harvest in a day using the unit rate formula.

Solution: Given:

Land harvested = 25 acres

Bushels of wheat harvested per acre = 25 × 350

= 8750 Bushels

Using the unit rate formula,

Bushels of wheat harvested per day = 8750 / 1

= 8750

Answer: Wheat harvested per day = 8750 Bushels

Ex.4.  If a shop offers you 3 books for Rs 90, what does the unit cost?

Solution:

To find: Unit cost of chocolates

Given:

Price of 3 books = Rs 90

Using the unit rate formula,

Per unit cost of chocolates = Price of books/ Number of books

= 90/3

= 30

Answer: Per unit cost of book = Rs 30.

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Q.1) What is the Unit of a in the Arrhenius Equation?

Answer: In the Arrhenius equation, A represents activation energy and this is the minimum energy needed for the reaction to occur. The unit of A in Arrhenius equation has to be expressed in joules per mole - not in kJ mol-1.

Q.2) What is the CFS to GPM Formula?

Answer: The CFS to GPM formula is

= x CFS/ 7.4805xGPM

Where,

CFS = Cubic feet per second

GPM = Gallons per minute

Q.3) What is the Rate Equation of Units of K?

Answer: The units of the rate constant, k, depending on the overall reaction order. The rate equation units of k for a zero-order reaction are M/s, the rate equation units of k for a first-order reaction are 1/s, and the units of k for a second-order reaction are 1/(M·s).

Hence the formula to find unit of rate constant is,

Rate = - d[A]/dt = k

Q.4) What is the Flow Rate Formula in Physics?

Answer: The flow rate formula is,

Q = vA

Where,

Q = volumetric flow rate

v = flow velocity

A = cross-sectional vector area

And the flow rate formula units is m3/s.

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