# Solve Fraction Problem: F2 = [ (v + v2)/(v + v1) ] F1

• sapiental
In summary, the conversation is about solving a physics problem involving fractions. The problem is to solve for v1 in the formula F2 = [(v + v2)/(v + v1)] F1, given the values for F2, v, v2, and F1. Suggestions for solving the problem are discussed, and the correct solution is provided as v1 = (F1(v+v2)/F2) - v.
sapiental
Hey,

I'm terrible with fractions and would appreciate any help regarding this problem.

This is a problem from my physics course.

F2 = [ (v + v2)/(v + v1) ] F1

I need to solve for v1. I am given the values for F2, v, v2, and F1 and need to turn the formula around to solve for v1..

F1 = 400
F2 = 420
v = 344
v2 = 26.82

My attempt was F2/(F1(v+v2)) = 1 / (v+v1)

but this is wrong..

any suggestions?

$$F_{2} = \left \frac{v+v_{2}}{v+v_{1}}\right F_{1}$$So $$F_{2}(v+v_{1}) = F_{1}(v+v_{2})$$

$$v + v_{1} = \frac{F_{1}(v+v_{2})}{F_{2}}$$

$$v_{1} = \frac{F_{1}(v+v_{2})}{F_{2}} - v$$

Last edited:

Sure, here is how to solve this problem:

First, let's simplify the fraction on the right side by multiplying both the numerator and denominator by (v+v1):

F2 = [ (v + v2)/(v + v1) ] F1

F2 = (v + v2) F1 / (v + v1)

Next, we can distribute the F1 to both terms in the numerator:

F2 = vF1 + v2F1 / (v + v1)

Now, we can rearrange the equation to isolate v1 on one side:

F2(v + v1) = vF1 + v2F1

F2v + F2v1 = vF1 + v2F1

F2v1 - vF1 = vF1 - vF1 + v2F1

F2v1 - vF1 = v2F1

Finally, we can divide both sides by F2 and then multiply by -1 to isolate v1:

-1(F2v1 - vF1) = -1(v2F1)

-v1 = -v2F1/F2

v1 = v2F1/F2

Therefore, the solution for v1 is:

v1 = (v2F1)/F2

Substituting in the given values, we get:

v1 = (26.82 * 400)/420

v1 = 25.54

So, v1 is approximately 25.54. I hope this helps! Remember to always check your work and plug the value of v1 back into the original equation to make sure it satisfies the problem. Good luck!

## What is the meaning of F1 and F2 in this equation?

F1 and F2 represent fractions in the equation. They are used to solve for the unknown value of v.

## What is the purpose of using fractions in this equation?

Fractions are used in this equation to represent the relationship between different variables. This allows for a more precise and accurate solution to the problem.

## What does the v1 and v2 stand for in this equation?

v1 and v2 represent two different values of the variable v. These values are used to determine the value of v in the equation.

## How do I solve this fraction problem?

To solve this fraction problem, you can use the algebraic method of cross multiplication. Multiply the numerator of F1 by the denominator of F2 and set it equal to the product of the numerator of F2 and denominator of F1. Then, solve for the variable v.

## What are some real-life applications of this type of problem?

This type of problem can be applied in various fields such as engineering, physics, and mathematics. For example, it can be used to calculate ratios in chemical reactions, determine distances in physics problems, or find a missing value in a mathematical equation.

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