Ask question

Ask question

All categories

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.

You might be interested in

PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!In two or more complete sentences explain how you would set up and solve the following eq

olchik [2.2K]

Peter's account is 910-40x, and Marla's account is 470-2x. This is a system, so you must find the number that makes both equations end up with the same number. Basically trial and error. Here is what I did:

Let's try the number 10. 910-400=510 and 470-20=450. I need a higher number.

Let's try 13 next. 910-520=390 and 470-26=444. Now the number has to be lower.

Let's try 12. 910-480=430 and 470-24=446. Close, and a little lower.

11.5 is too low, and 11.7 is too high. 11.6 has Equation 1 at 446 and Equation 2 at 446.8. Very close!

It is somewhere around 11.6. I hope that this can give you a start in figuring it out, because I don't believe in giving the complete answer, because then you do not learn anything from it.

4 0

3 years ago

Read 2 more answers

You randomly draw a marble from a bag. You then put it back before drawing a second marble. These events are ________ events. an

Mkey [24]

I would assume Independent because pulling 1 marble doesn't cause you to pull a second one.

4 0

2 years ago

Read 2 more answers

The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If th

zlopas [31]

Answer:

$P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)$

And we can find this probability with the complement rule:

$P(Z>-1)=1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the average homicide rate for the cities of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,2)$

Where $\mu=10$ and $\sigma=2$

We are interested on this probability

$P(X>8)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)$

And we can find this probability with the complement rule:

$P(Z>-1)=1-P(Z$

5 0

3 years ago

A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a c

SpyIntel [72]

Check the picture below.

$\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lccclll}
P(x) = &{{ -0.05}}x^2&{{ +500}}x&{{ -100000}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)\\\\
-------------------------------\\\\
\textit{so }-\cfrac{b}{2a}\textit{ units maximize the profit, and}\\\\\\
c-\cfrac{b^2}{4a}\textit{ dollars is the maximum profit}$

5 0

2 years ago

Give the values of a, b, and c needed to write the equation's standard form.(5 + x)(5 - x) = 7A = 1; B = 0; C = -18A = 25; B = 0

Maksim231197 [3]

We need to FOIL that out and then get it into standard form to see what our A, B, and C are. FOILing gives us $25-x^2=7$ . If we move the 7 over by subtraction and set it equal to 0, we have $-x^2+18=y$ . In order to avoid a negative leading coefficient, we can change all the signs to get $x^2-0x-18=0$ so A = 1, B = 0, C = -18, first choice above.

5 0

2 years ago