8. Equations Involving Fractions
In this section, we can find the solution easily by multiplying throughout by the lowest common denominator.
Example 1:
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:
So we have:
So
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:
For a particular circuit, the combined resistance R was found to be 4 ohms (W), and R1= 10 W. Find R2.
Answer:
We have:
We need to multiply throughout by the lowest common denominator: 20R2
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?
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