Question

A car is traveling at a rate of 27 miles per hour. What is the car's rate in feet per second? How many feet will the car travel in 2 seconds? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers.

Answer 1

@TeddySized could you help me please?

Answer 2

It changed to 27 miles per hour and 2 seconds

Answer 3

@DontLikeMathButOhWell can you help?

Answer 4

To change from one unit to another, you multiply by the appropriate fraction:

1 mile = 5280 feet
So to go from miles to feet, we multiply our quantity in miles by 5280 feet / 1 mile

\[27 \text{ miles} = 27 \cancel{\text{ miles}} * (\frac{5280 \text{ feet}}{1 \cancel{\text{ mile}}}) = 142560\text{ feet}\]

Answer 5

Similarly, to convert from hours to seconds, we use the relationships \[1 \text{ hour} = 60 \text{ minutes}\]and\[1 \text{ minute} = 60 \text{ seconds}\]giving us
\[1 \text{ hour} = 1 \cancel{\text{ hour}} * (\frac{60 \cancel{\text{ minutes}} }{ 1 \cancel{\text{ hour}}}) * (\frac{60 \text{ seconds}}{ 1 \cancel{\text{ minute}}}) = 3600 \text{ seconds}\]

Answer 6

So is that the answer?

Answer 7

So \[27 \text { miles}/ \text{hour} = 27 \frac{\text{miles}}{\text{hour}}*(\frac{1 \text{ hour}}{3600 \text{ seconds}})*(\frac{5280 \text{ feet}}{1 \text{ mile}}) = \]\[=27 \frac{\cancel{\text{miles}}}{\text{hour}}*(\frac{1 \text{ hour}}{3600 \text{ seconds}})*(\frac{5280 \text{ feet}}{1 \cancel{\text{ mile}}}) =\]\[=27 \frac{\cancel{\text{miles}}}{\cancel{\text{hour}}}*(\frac{1 \cancel{\text{ hour}}}{3600 \text{ seconds}})*(\frac{5280 \text{ feet}}{1 \cancel{\text{ mile}}}) =\]\[=27 *(\frac{5280}{3600})*(\frac{\text{ feet}}{ {\text{ second}}}) =\]

Answer 8

And in 2 seconds, you'll go
\[27*\frac{5280}{3600}\frac{\text{ feet}}{\cancel{\text{ second}}} * 2 \cancel{\text{ seconds}} = \]

Answer 9

Doing it with the units this way, and making sure to do the cancelation of units carefully acts as a strong safety net to avoid mistakes. If you end up with a weird unit, you've almost certainly done it wrong.

Answer 10

I'm confused as to what the answer is for the speed and the distance traveled in 2 seconds

Answer 11

I didn't tell you what the answers were, I showed you the procedure for getting them.

Answer 12

You just have to do the arithmetic at this point to write down the answer on the right side of the equals sign, that isn't too much to ask, is it? :-)

Answer 13

Haha I mean it's always easier to just get the answer….but thank you!

Answer 14

Hopefully I don't mess it up. I only have one chance to answer it correctly.

Answer 15

it's maybe easier this time, but it will be a whole lot harder on the test when I'm not there :-)

Answer 16

do it, and show me your answer, and I'll check it for you.

Answer 17

Who says you won't be there?! Haha

Answer 18

As a ballpark number, not so much useful for finding the answers in this problem as just for checking the reasonability of an answer, I always remember that 60 mph = 88 feet/second. So, at 27 mph, you're going about half of that, so your answer should be about half of 88 feet/second. If you come up with say 973.6 feet per second, it would be good to take another look.

Answer 19

and for the second problem, if we're going about 40 feet per second, roughly, then in 2 seconds we should go about 80 feet, roughly.

Answer 20

it's a valuable skill to be able to make estimates and judge the reasonability of any answer you get (or judge the reasonability of something you read or are told, too!)

Answer 21

I put 44 and 80. It was incorrect.

Answer 22

I am horrible at math. As you can see..

Answer 23

no, no, no, I didn't tell you those were the answers! I said they were ballpark estimates!!!

Answer 24

Sigh.

Answer 25

Back to what I wrote earlier:
27 mph in ft per second:
\[=27 *(\frac{5280}{3600})*(\frac{\text{ feet}}{ {\text{ second}}}) =\]Get out your calculator or scratch paper or whatever and calculate 27*5280, and divide the result by 3600. That is 27 mph in feet per second. If you do it correctly, you'll see that the answer is very close to 40 (but not exactly 40).

Answer 26

Then, to find the distance covered in 2 seconds:
\[27*\frac{5280}{3600}\frac{\text{ feet}}{\cancel{\text{ second}}} * 2 \cancel{\text{ seconds}} =\]Multiply 27*5280, divide by 3600, multiply by 2. Again, if done correctly, the answer will be quite close to 80.

Give me the two numbers you get and I'll tell you if you did it correctly.

Answer 27

I'm sorry you entered the wrong numbers, but I did tell you what to do...

Answer 28

Yes.

Answer 29

So, what do you get when you do those computations?

Answer 30

I'm sorry I was offline. Do you still need my help tho?