8. Equations Involving Fractions

In this section, we can find the solution easily by multiplying throughout by the lowest common denominator.


Example 1:

math expression

An aquarium can be filled by one hose in 7 minutes and a second hose in 10 minutes. How long will it take to fill the tank if both hoses operate together?



Answer:

Since each hose makes the filling time less, we have to add the reciprocals together and take the reciprocal of the result.

We need to use:

math expression

So we have:

math expression

math expression

So

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So it will take 4.1 minutes to fill the tank with both hoses operating together.

 

Example 2:

For 2 resistors with resistances R1and R2 in parallel, the combined resistance R is given by:

math expression

For a particular circuit, the combined resistance R was found to be 4 ohms (W), and R1= 10 W. Find R2.

 

Answer:

We have:

math expression

We need to multiply throughout by the lowest common denominator: 20R2

math expression

 

Example 3:

A car averaged 30 km/h going from home to work and 40 km/h on the return journey. If the total time for the two journeys is 50 minutes, how far is it from home to work?


Answer



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