Worksheet: Applications of Rational Equations

In this worksheet, we will practice using rational equations to solve problems set in real-life contexts.

Q1:

A container holds 100 mL of a solution that is 25 mL acid. If 𝑛 mL of a solution that is 6 0 % acid is added, the function 𝐶 gives the concentration, 5 0 % , as a function of the number of milliliters added, 𝐶 = 2 5 + 0 . 6 𝑛 1 0 0 + 𝑛 . Express 𝑛 as a function of 𝐶 and determine the number of milliliters needed to have a solution that is 6 0 % acid.

  • A 𝑛 = 2 5 + 1 0 0 𝐶 𝐶 + 0 . 6 , 68 mL
  • B 𝑛 = 1 0 0 𝐶 2 5 𝐶 , 50 mL
  • C 𝑛 = 1 0 0 𝐶 2 5 𝐶 + 0 . 6 , 23 mL
  • D 𝑛 = 1 0 0 𝐶 2 5 0 . 6 𝐶 , 250 mL
  • E 𝑛 = 1 0 0 𝐶 + 2 5 0 . 6 𝐶 , 750 mL

Q2:

Liam went on a bike ride of 48 miles. He realized that if he had gone 4 mph faster, then he would have arrived 6 hours sooner. How fast did he actually ride?

Q3:

If Victoria does a job in 10 hours, and with the help of Scarlett, they can do it together in 6 hours, how long would it take Scarlett to do it alone?

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