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Suma drove a distance of 150 km in 2 hours and 30 minutes. a) Find its speed in km/h. b) Find his speed in m/second.

Mathematics

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3 parts
a

60 km/h\text{60 km/h}

b

16.67 m/s\text{16.67 m/s}

4

-3∘C\text{-3}^\circ\text{C}

Step-by-step solution

6 steps

Here are the solutions to the problems.

Part 23

Suma drove a distance of 150 km150 \text{ km} in 2 hours2 \text{ hours} and 30 minutes30 \text{ minutes}.

Part a

60 km/h\text{60 km/h}

Find its speed in km/h\text{km/h}.

  1. Convert the total time to hours.

    Time=2 hours+30 minutes\text{Time} = 2 \text{ hours} + 30 \text{ minutes} 30 minutes=3060 hours=0.5 hours30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} Total time=2 hours+0.5 hours=2.5 hours\text{Total time} = 2 \text{ hours} + 0.5 \text{ hours} = 2.5 \text{ hours}

  2. Calculate the speed using the formula Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}.

    Speed=150 km2.5 hours\text{Speed} = \frac{150 \text{ km}}{2.5 \text{ hours}} Speed=60 km/h\text{Speed} = 60 \text{ km/h}

    The speed in km/h\text{km/h} is 60 km/h\boxed{\text{60 km/h}}.

Part b

16.67 m/s\text{16.67 m/s}

Find his speed in m/second\text{m/second}.

  1. Convert the speed from km/h\text{km/h} to m/s\text{m/s}.

    We know that 1 km=1000 m1 \text{ km} = 1000 \text{ m} and 1 hour=3600 seconds1 \text{ hour} = 3600 \text{ seconds}.

    Speed=60kmh×1000 m1 km×1 h3600 s\text{Speed} = 60 \frac{\text{km}}{\text{h}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} Speed=60×10003600ms\text{Speed} = \frac{60 \times 1000}{3600} \frac{\text{m}}{\text{s}} Speed=600003600ms\text{Speed} = \frac{60000}{3600} \frac{\text{m}}{\text{s}} Speed=60036ms\text{Speed} = \frac{600}{36} \frac{\text{m}}{\text{s}} Speed=1006ms\text{Speed} = \frac{100}{6} \frac{\text{m}}{\text{s}} Speed=16.67ms(rounded to two decimal places)\text{Speed} = 16.67 \frac{\text{m}}{\text{s}} \quad (\text{rounded to two decimal places})

    The speed in m/s\text{m/s} is 16.67 m/s\boxed{\text{16.67 m/s}}.

Part 4

-3∘C\text{-3}^\circ\text{C}

The initial temperature reading on a thermometer was −6∘C-6^\circ\text{C}. The temperature dropped by 5∘C5^\circ\text{C} and rose by 8∘C8^\circ\text{C}. Use a number line to find the final temperature.

  1. Start with the initial temperature.

    Initial temperature=−6∘C\text{Initial temperature} = -6^\circ\text{C}

  2. The temperature dropped by 5∘C5^\circ\text{C}.

    Temperature after drop=−6∘C−5∘C=−11∘C\text{Temperature after drop} = -6^\circ\text{C} - 5^\circ\text{C} = -11^\circ\text{C}

  3. The temperature rose by 8∘C8^\circ\text{C}.

    Final temperature=−11∘C+8∘C=−3∘C\text{Final temperature} = -11^\circ\text{C} + 8^\circ\text{C} = -3^\circ\text{C}

    The final temperature is -3∘C\boxed{\text{-3}^\circ\text{C}}.

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