Question

The following equation represents the average rate for the trip. Is this equation equivalent to the one you wrote above? Explain why or why not.

Equation: (2d) / (d/r1) + (d/r2)
My Equation: r1t1 + r2t2 / t1 +t2

I'm just having trouble seeing if they are similar or not. Thank you for the help! <3

Answer 1

The two equations are similar and they may or may not be equivalent

How to determine if the equations are equivalent?

The equations are given as:

$\frac{2d}{d/r_1 + d/r_2}$

$\frac{r_1t_1 + r_2t_2}{t_1 + t_2}$

Rewrite the first equation as:

$2d \div (\frac{d}{r_1} + \frac{d}{r_2})$

Take the LCM

$2d \div \frac{dr_2 + dr_1}{r_1r_2}$

Express as product

$2d \times \frac{r_1r_2}{dr_2 + dr_1}$

Cancel out the common factor

$2 \times \frac{r_1r_2}{r_2 + r_1}$

Evaluate the product

$\frac{2r_1r_2}{r_2 + r_1}$

Express the numerator as a sum

$\frac{r_1r_2 + r_1r_2}{r_2 + r_1}$

By comparing $\frac{r_1r_2 + r_1r_2}{r_2 + r_1}$ and the second equation $\frac{r_1t_1 + r_2t_2}{t_1 + t_2}$, we can see that both equations are similar and they may or may not be equivalent

Read more about equivalent equations at:

https://brainly.com/question/2972832

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