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skelet666 [1.2K]

2 years ago

10

You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate on the return t

rip is 30 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 2 hours, use a rational equation and factoring to find your average rate on the outgoing trip to work?

1 answer:

boyakko [2]2 years ago

6 0

Answer:

The average rate on the outgoing trip is 30 miles per hour.

Step-by-step explanation:

Consider the provided information.

You commute to work a distance of 40 miles and return on the same route at the end of the day.

Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 2 hours.

Let the average rate on the outgoing trip is x

Average rate on the return trip = x+30

As we know $Time=\frac{Distance}{Speed}$

$\frac{40}{x}+ \frac{40}{(x+30)} = 2$

$\frac{40(x+30)+40x}{x(x+30)}= 2$

$40x+1200+40x= 2(x^2+30x)$

$80x+1200= 2x^2+60x$

$2x^2-20x-1200=0$

$x^2-10x-600=0$

$x^2-30x+20x-600=0$

$(x-30)(x+20)=0$

The value of x can't be a negative number so x=30

Hence, the average rate on the outgoing trip is 30 miles per hour.

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68.5% seats filled

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Step-by-step explanation:

<h3><u>General outline</u></h3>

Identify the whole and the part
Change ratio into a percentage

<h3><u>Ratios</u></h3>

Percentages are formed when one finds a ratio of two related quantities, usually comparing the first partial quantity to the amount that "should" be there.

$\text{ratio}=\dfrac {\text{the "part"}}{\text{the whole}}$

For instance, if you have a pie, and you eat half of the pie, you're in effect imagining the original pie (the whole pie) cut into two equal pieces, and you ate one of them (the "part" of a pie that you ate). To find the ratio of pie that you ate compared to the whole pie, we compare the part and the whole:

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If you had instead eaten three-quarters of the pie, you're in effect imagining the original pie cut into 4 equal pieces, and you ate 3 of them.

$\text{ratio}=\dfrac {\text{the number of "parts" eaten}}{\text{the number of parts of the whole pie}}$

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There can be cases where the "part" is bigger than the whole. Suppose that you are baking pies and we want to find the ratio of the pies baked to the number that were needed, the number of pies you baked is the "part", and the number of pies needed is the whole. This could be thought of as the ratio of project completion.

If we need to bake 100 pies, and so far you have only baked 75, then our ratio is:

$\text{ratio}=\dfrac {\text{the number of "parts" made}}{\text{the number of parts of the whole order}}$

$\text{ratio}=\dfrac {75}{100}$

But, suppose you keep baking pies and later you have accidentally made more than the 100 total pies.... you've actually made 125 pies. Even though it's the bigger number, the number of pies you baked is still the "part" (even though it's bigger), and the number of pies needed is the whole.

$\text{ratio}=\dfrac {\text{the number of "parts" made}}{\text{the number of parts of the whole order}}$

$\text{ratio}=\dfrac {125}{100}$

<h3><u>Percentages</u></h3>

To find a percentage from a ratio, there are two small steps:

Divide the two numbers
Multiply that result by 100 to convert to a percentage

<u>Going back to the pies:</u>

When you ate half of the pie, your ratio of pie eaten was $\frac{1}{2}$

Dividing the two numbers, the result is $0.5$

Multiplying by 100 gives 50. So, the percentage of pie that you ate (if you ate half of the pie) is 50%

When you ate three-quarters of the pie, the ratio was $\frac{3}{4}$

Dividing the two numbers, the result is 0.75

Multiplying by 100 gives 75. So, the percentage of pie that you ate (if you ate three-quarters of the pie) is 75%.

When you were making pies, and 100 pies were needed, but so far you'd only baked 75 pies, the ratio was $\frac{75}{100}$

Dividing the two numbers, the result is 0.75

Multiplying by 100 gives 75. So, the percentage of the project that you've completed at that point is 75%.

Later, when you had made 125 pies, but only 100 pies were needed, the ratio was $\frac{125}{100}$

Dividing the two numbers, the result is 1.25

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<h3><u>The questions</u></h3>

<u>1. 27400 spectators n a 40000 seat stadium percentage.</u>

Here, it seems that the question is asking what percentage of the stadium is full, so the whole is the 40000 seats available, and the "part" is the 27400 spectators that have come to fill those seats.

$\text{ratio}=\dfrac {\text{the number of spectators filling seats}}{\text{the total number of seats in the stadium}}$

$\text{ratio}=\dfrac {27400}{40000}$

Dividing gives 0.685. Multiplying by 100 gives 68.5. So, 68.5% of the seats have been filled.

<u>2. an archer scores 95 points out of a possible 125 points percentage</u>

Here, it seems that the question is asking what percentage of the points possible were earned, so the whole is the 125 points possible, and the "part" is the 95 points that were earned.

$\text{ratio}=\dfrac {\text{the number of points earned}}{\text{the total number of points possible}}$

$\text{ratio}=\dfrac {95}{125}$

Dividing gives 0.76. Multiplying by 100 gives 76. So, 76% of points possible were earned.

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