Question

A small plane flies 760,320 yards in 2 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work. Part A: Rearrange the distance formula, d = rt, to solve for rate. (2 points) Part B: Find the plane's rate in yards per hour. (3 points) Part C: Find the plane's rate in miles per hour. (3 points) Part D: Which unit, yards, or miles, makes more sense to use in this scenario, and why? (2 points) Please explain in steps

Answer 1

Answer:

See below.

Step-by-step explanation:

So we know that a small plane flies 760,320 yards in 2 hours.

A)

The distance formula is:

$d=rt$

To solve for the rate r, divide both sides by t:

$r=\frac{d}{t}$

B)

To find the rate in yards per hour, divide the amount of yards traveled by the amount of hours it took. Thus:

$r=\frac{\text{760320 yards}}{\text{2 hours}}$

Divide:

$r=\text{380160 yd/hr}$

So, the plane travels at a rate of 380,160 yards per hour.

C)

There are 1,760 yards in a mile.

To find the plane's rate in mile per hour, we can use dimensional analysis.

First, we know that the rate is 380,160 yards per hour:

$r=\frac{\text{380160 yards}}{\text{1 hour}}$

We want to cancel out "yards" in the numerator. Thus, let's multiply by 1 mi over 1,760 yards. Thus:

$r=\frac{\text{380160 yards}}{\text{1 hour}}\cdot \frac{\text{1 mi}}{\text{1760 yards}}$

The yards will cancel:

$r=\frac{\text{380160}}{\text{1 hour}}\cdot \frac{\text{1 mi}}{\text{1760}}$

Multiply straight across:

$r=\frac{\text{380160 mi}}{\text{1760 hour}}$

Divide:

$r=\frac{\text{216 miles}}{\text{ hour}}$

So, the plane's rate is 216 miles per hour.

D)

Miles make more sense in this scenario. This is because the distance covered is too vast to be appropriately conveyed using yards. 380,160 yards per hour is simply too much, while 216 miles per hour is much easier to comprehend.