Remaining fractions, rates, recurring decimals and rational relationships
Free examples and worked answers. No account needed.
Practise the method.
Remaining fractions, rates, recurring decimals and rational relationships
Optional enrichment: Remaining fractions, rates, recurring decimals and rational relationships
Example 1
Pump A takes x hours to fill a tank; pump B takes 5 hours longer. Starting with an empty tank, A runs alone for 4 hours. B then joins A, and they finish filling the tank in a further 2370 hours. Find x, with x>4. Both pumps run at constant rates.
Show worked answer
Answer: 9
The filled fractions give x4+(2370)(x1+x+51)=1.
Clear the denominators and solve the quadratic;
its positive root is x=9 hours.
Example 2
Two positive numbers differ by 6. The reciprocal of the smaller minus the reciprocal of the larger is 203. Find the larger number.
Show worked answer
Answer: 10
Let the larger be x.
Then x−61−x1=203.
Combine the fractions and solve the resulting quadratic.
The root with x>6 is 10.
Example 3
Pump A takes x hours to fill a tank; pump B takes 2 hours longer. Starting with an empty tank, A runs alone for 3 hours. B then joins A, and they finish filling the tank in a further 67 hours. Find x, with x>3. Both pumps run at constant rates.
Show worked answer
Answer: 5
The filled fractions give x3+(67)(x1+x+21)=1.
Clear the denominators and solve the quadratic;
its positive root is x=5 hours.
Put it into practice.
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