Find the Unit Rate: Detailed Solutions to Questions

The concept of rate in maths and algebra is an important one. Detailed solutions to the questions on finding rate are presented.

Find the unit rate in each of the following situations.

  1. I travelled 300 kilometers in 5 hours. Find the unit rate in kilometers/hour.

    Solution

    The unit rate is the distance divided by the time: \[ \dfrac{300 \ \text{kilometers}}{5 \ \text{hours}} = \left(\dfrac{300}{5}\right) \ (\text{km/hour}) = 60 \ \text{km/hour}. \] Note: This unit rate is also called speed.

  2. An international phone call costs $10 for 4 minutes. Find the unit rate in dollars/minute.

    Solution

    \[ \dfrac{10 \ \text{dollars}}{4 \ \text{minutes}} = \left(\dfrac{10}{4}\right) \ (\text{dollars/minute}) = 2.5 \ \text{dollars/minute}. \]

  3. Joelle reads 18 pages in 9 minutes. Find the unit rate in pages/minute.

    Solution

    \[ \dfrac{18 \ \text{pages}}{9 \ \text{minutes}} = \left(\dfrac{18}{9}\right) \ (\text{pages/minute}) = 2 \ \text{pages/minute}. \]

  4. A car consumes 12 gallons of fuel for a distance of 240 miles. Find the unit rate in miles/gallon.

    Solution

    \[ \dfrac{240 \ \text{miles}}{12 \ \text{gallons}} = \left(\dfrac{240}{12}\right) \ (\text{miles/gallon}) = 20 \ \text{miles/gallon}. \]

  5. A pump moves 45 liters of water every 5 minutes. What is the unit rate of the pump in liters/minute?

    Solution

    \[ \dfrac{45 \ \text{liters}}{5 \ \text{minutes}} = \left(\dfrac{45}{5}\right) \ (\text{liters/minute}) = 9 \ \text{liters/minute}. \]

  6. Joe bought 4 kilograms of apples at the cost of $16. Find the unit rate (or price of 1 kilogram) in dollars/kilogram.

    Solution

    \[ \dfrac{16 \ \text{dollars}}{4 \ \text{kilograms}} = \left(\dfrac{16}{4}\right) \ (\text{dollars/kilogram}) = 4 \ \text{dollars/kilogram}. \]

  7. Which moves faster, an object A that moves 15 centimeters every 5 seconds or an object B that moves 24 centimeters every 8 seconds?

    Solution

    Find the unit rate for each object: \[ \text{Object A: } \dfrac{15}{5} = 3 \ \text{cm/second}, \qquad \text{Object B: } \dfrac{24}{8} = 3 \ \text{cm/second}. \] Both objects move at the same speed.

  8. Car A consumes 12 gallons of fuel for a distance of 240 miles. Another car B consumes 25 gallons for a distance of 550 miles. Which of the two cars travels further per gallon?

    Solution

    \[ \text{Car A: } \dfrac{240}{12} = 20 \ \text{miles/gallon}, \qquad \text{Car B: } \dfrac{550}{25} = 22 \ \text{miles/gallon}. \] Car B travels further per gallon.

  9. Convert the unit rate \(60\) kilometers/hour into kilometers/minute.

    Solution

    Since \(1 \ \text{hour} = 60 \ \text{minutes}\), \[ 60 \ \dfrac{\text{km}}{\text{hour}} = \dfrac{60}{60} \ \dfrac{\text{km}}{\text{minute}} = 1 \ \text{km/minute}. \]

  10. Convert the unit rate \(72\) kilometers/hour into meters/second.

    Solution

    Since \(1 \ \text{km} = 1000 \ \text{m}\) and \(1 \ \text{hour} = 3600 \ \text{seconds}\), \[ 72 \ \dfrac{\text{km}}{\text{hour}} = \dfrac{72 \times 1000}{3600} \ \dfrac{\text{m}}{\text{second}} = 20 \ \text{m/second}. \]

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