Question

convert each rate using dimensional analysis. round to the nearest tenth if necessary.

30mi/h=_____ ft/min
a.2640
b.264
c.880
d.2112

Answer 1

I do not know what to do can someone pease help me

Answer 2

I'll help you with dimensional analysis.

First, you need to know the conversions factors.
How many feet are in 1 mile?
How many minutes are in 1 hour?

Answer 3

ok so there are 5,280 feet in a mile and 60 min in 1 hour

Answer 4

is that correct?

Answer 5

Yes, that's great.

The basis of dimensional analysis for unit conversion is the facft that multiplying a number by 1 does not change the number.
For example, 3 * 1 = 3
1.34 * 1 = 1.34
This is the multiplicative property of 1.

Answer 6

The conversions you wrote are correct.

5280 ft = 1 mile is a true statement.
From the division property of equality (both sides of an equation can be divided by the same nonzero number), we can divide the equation
5280 ft = 1 mi
by 5280 ft:

\(\dfrac{5280 ~ft}{5280 ~ft} = \dfrac{1 ~mi}{5280 ~ft} \)

which simplifies to

\(1 = \dfrac{1 ~mi}{5280~ft} \)

Notice that \(\dfrac{1~mi}{5280 ~ft} \) is a fraction that is equal to 1.

Answer 7

Since the reciprocal of 1 is also 1, and since \(\dfrac{1~mi}{5280~ft} \) is equal to 1, then the reciprocal of \(\dfrac{1~mi}{5280~ft} \), which is \(\dfrac {5280~ft} {1~mi} \), is also equal to 1.

Are you following so far?

Answer 8

The same can be done for the conversion of 1 hour into 60 minutes.

\(1 ~hr = 60~min\)

\( \dfrac{1~hr}{60~min} = \dfrac{60~min}{1~hr} = 1 \)

Answer 9

Now that we have the conversion factors written as fractions that equal 1, we begin the dimensional analysis part of the conversion of units.

We take the original number with the given untis and convert it into the desired units by a performing a series of multiplications by 1, but 1 is written in the way that will yield the units we want and will cancel out the units we don't want. We can do this since multiplying a number by 1 does not change the number.

Answer 10

Here is the first example:

\( 30 \dfrac{\color{red}{mi}}{\color{blue}{hr}} \times \dfrac{5280~ft}{1~\color{red}{mi}} \times \dfrac{1~\color{blue}{hr}}{60~min} \)

\( = 30 \dfrac{\cancel{\color{red}{mi}}}{\cancel{\color{blue}{hr}}} \times \dfrac{5280~ft}{\cancel{1~\color{red}{mi}}} \times \dfrac{\cancel{1~\color{blue}{hr}}}{60~min} \)

\(= \dfrac{30 \times 5280}{60} \dfrac{ft}{min} \)

Just multiply the numbers together.