Mathematics, 09.11.2020 16:40, myahlit84

You are running a fuel economy study. One of the cars you find is blue. It can travel 44 1/2 gallons of gasoline. Another car is red. It can travel 25 3/5 on 4/5 gallons of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?

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answered: ericavasquez824

Question:

You are running a fuel economy study. One of the cars you find is blue. It can travel $44\frac{1}{2}$ miles on $1\frac{1}{4}$ gallons of gasoline.

Another car is red. It can travel $25\frac{3}{5}$ on $\frac{4}{5}$ gallon of gasoline.

What is the unit rate for miles per gallon for each car?

Which car could travel the greater distance on 1 gallon of gasoline?

(a)

$Rate = 35\frac{3}{5}\ miles\ per\ gallon$

$Rate = 32\ miles\ per\ gallon$

(b)

The blue car will travel faster

Step-by-step explanation:

Given

Blue Car:

$Distance = 44\frac{1}{2}\ miles$

$Gasoline = 1\frac{1}{4}\ gallons$

Red Car

$Distance = 25\frac{3}{5}\ miles$

$Gasoline = \frac{4}{5}\ gallons$

Solving (a):

This is solved by dividing the distance travelled by the amount of gasoline.

i.e.

Rate = Distance/Gasoline

Blue Car:

$Rate = 44\frac{1}{2} / 1\frac{1}{4}$

$Rate = \frac{89}{2} / \frac{5}{4}$

$Rate = \frac{89}{2} * \frac{4}{5}$

$Rate = \frac{89}{1} * \frac{2}{5}$

$Rate = \frac{89 * 2}{1 * 5}$

$Rate = \frac{178}{5}$

$Rate = 35\frac{3}{5}\ miles\ per\ gallon$

Red Car:

$Rate = 25\frac{3}{5}/\frac{4}{5}$

$Rate = \frac{128}{5}/\frac{4}{5}$

$Rate = \frac{128}{5} * \frac{5}{4}$

$Rate = \frac{128 * 5}{5 * 4}$

$Rate = \frac{128}{4}$

$Rate = 32\ miles\ per\ gallon$

(b)

In (a), we have:

$Rate = 35\frac{3}{5}\ miles\ per\ gallon$ --- Blue Car

$Rate = 32\ miles\ per\ gallon$ --- Red Car

By comparison:

The rate of the blue car is greater than that of the red

Hence, the blue car will travel faster

answered: Guest

9.8? i'm not really sure

answered: Guest

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder: $652=5q+r$

here $q$ ("q" for quotient) is the number of brownies each of your friends get, and $r$ is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so $q=130$ and $r=2$ .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.