9.5Speed, Distance and Time

Speed is distance per unit time, and the three are locked together.

The three quantities, in one arrangement.

Cover $D$ : multiply, $S \times T$
Cover $S$ : divide, $D \div T$
Cover $T$ : divide, $D \div S$

Changing km/h into m/s

$1$ h : $1$ km
$1$ h : $1000$ m
$3600$ s : $1000$ m
$1$ s : $\dfrac{1000}{3600}$ m

MRT speed conversion

An MRT train travels at 72 km/h between stations. Convert this speed to m/s.

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1

\to

72

1

\to

72\,000

3600

\to

72\,000

1

\to

\dfrac{72\,000}{3600}

= 20 \text{ m}

So the speed is

20

m/s.

Average speed over two legs

Priya cycles $\displaystyle 15$ km to a park at $\displaystyle 10$ km/h and returns at $\displaystyle 6$ km/h. Find her average speed for the whole trip.

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\displaystyle \text{Time for outward trip}

\displaystyle = \dfrac{15}{10}

\displaystyle = 1.5 \text{ h}

\displaystyle \text{Time for return trip}

\displaystyle = \dfrac{15}{6}

\displaystyle = 2.5 \text{ h}

\displaystyle \text{Total distance}

\displaystyle = 15 + 15

\displaystyle = 30 \text{ km}

\displaystyle \text{Total time}

\displaystyle = 1.5 + 2.5

\displaystyle = 4 \text{ h}

\displaystyle \text{Average speed}

\displaystyle = \dfrac{30}{4}

\displaystyle = 7.5 \text{ km/h}

Reverse speed: finding time for a different distance

A car covers $\displaystyle 195$ km in $\displaystyle 2.5$ hours. At the same speed, how long does $\displaystyle 312$ km take?

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\displaystyle \text{Speed}

\displaystyle = \dfrac{195}{2.5}

\displaystyle = 78 \text{ km/h}

\displaystyle \text{Time for 312 km}

\displaystyle = \dfrac{312}{78}

\displaystyle = 4 \text{ hours}

Now you try

A train travels $500$ km at a speed of $100$ km/h. How many hours does the journey take?

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\displaystyle T

\displaystyle = \frac{D}{S}

\displaystyle = \frac{500}{100}

\displaystyle = 5 \text{ hours}

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