Application of speed, distance and time

Last updated: September 21, 2021  | 


Application of speed, distance and time problems

Speed, distance and time problems are interesting because they often describe simple situations which people confuse with the wrong formulas. It is also important that in these types of questions, the objects move at constant or average speeds in speed, distance and time scenarios.


E1.11: Calculate average speed

Speed ​​is directly related to two other variables: Distance and time. Speed ​​is distance divided by time, expressed as follows:

$$\text{Speed (m/s)}=\frac{\text{distance (m)}}{\text{time(s)}}$$

Speed, distance and time

The time relationship with the other two variables, which divide the distance by the speed. Its expression is as follows:

$$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$$

Speed is beside time. So, there is no doubt that distance is speed multiplied by time.


Worked examples

Example 1: Albert and Danny participate in a long distances race. Albert runs at $$6\text{miles per hour}$$, while Danny runs at $$5\text{miles per hour}$$. They run at a constant speed throughout the race when Danny reaches $$25\text{miles}$$. Albert is exactly $$40\text{minutes}$$ away from finishing. What is the distance in miles?

Step 1: Write the given values.

The distance is $$25\text{miles}$$, and the speed is $$5\text{miles per hour}$$.

Step 2: Recall the formula for the time.

$$\text{Time}=\frac{\text{distance}}{\text{speed}}$$

Step 3: Substitute the values in the formula.

$$\text{Time}=\frac{25\text{ miles}}{5\text{miles per hour}}=5\text{hours}

Step 4: Write Albert finishing time in hours. 

Albert is exactly $$40\text{minutes}$$ away from finishing.

So, Albert will take $$5\text{hours}+40\text{minutes}$$ or $$\frac{17}{3}\text{hours}$$ to finish the race.

Step 5: Recall the formula for the distance.

$$\text{Distance}=\text{speed} \times \text{time}$$

Step 6: Substitute the values in the formula.

$$\text{Distance}=\left(6\text{ miles per hour} \right)\times \left(\frac{17}{3}\text{hours} \right)=34\text{miles} $$.

So, the race distance is $$34\text{miles}$$


E1.14 A: Calculate times in terms of the $$24\text{ hours}$$ and $$12\text{ hours}$$ clock.

The $$12$$-hour clock is most often represented, by the number $$1-12$$, on an analogue clock. On the digital clock, it shows a.m (ante meridiem) or p.m (post meridiem).

The $$24$$-hour clock is more often shown in digital clocks and is written in $$4$$ digits form, with the first two digits representing the hour and the last two representing the minutes. There is no need for a.m or p.m; because each time represents each hour in a day.


Worked example

Example 1: Write the times in $$24$$-hour clock: $$3:06\text{a.m}$$ and $$8:14\text{p.m}$$

Step 1: Recall the $$24$$-hour clock system.

In the $$24$$-hour clock system, the first two digits represent the hours, and the last two digits represent the minutes.

Step 2: Write the time in $$24$$-hour clock, $$3:06\text{a.m}$$.

This is $$3$$-hours from the beginning of the day, so the $$24$$-hour time is $$0306$$.

Step 3: Write the time in $$24$$-hour clock, $$8:14\text{p.m}$$.

This is $$20$$ hours ($$12$$+$$8$$) from the beginning of the day, so the $$24$$-hour time is $$2014$$.


E1.14 B: Read clocks, dials and timetables

The figure given below will help us to read a clock.

How to read clocks

In the figure, the hour-hand indicates the number $$1$$ or after $$1$$. So, we read it as $$i\text{hour}$$. The minute hand indicates $$4$$ divisions after the number $$3$$. That is $$3\times 5+4=19$$ or $$19$$ divisors from $$12$$. So, we read it as $$19\text{minutes}$$.

The clock indicates that the time is $$1\text{hour } 19\text{minutes}$$.

Read the dials from left to right. If the pointer is between two numbers, always take the lower number. 

If the pointer falls between $$9$$ and $$0$$, write down $$9$$.

Read a timetable; you first locate the column for the location you are interested in. Then you look for a time you are suitable for to get to wherever you need to go on time. You then look at the other columns for the row to find out when you will arrive at your desired location.


Worked example

Example 1: There are two images of the clock given to Rajesh. He needs to find out which clock shows $$10:45$$. And which clock shows $$10:30$$.

Time question with 2 clocks

Step 1: Write the time.

The first clock’s hour hand crossed $$10$$ and the minute hand is on $$9$$, which means the time displayed by the clock is $$10:45$$. On the other hand, the second clock’s hour hand crossed $$10$$ and the minute hand is on $$6$$, which means the time displayed by the clock is $$10:30$$.

So, the first clock represents $$10:45$$, while the second clock represents $$10:30$$.

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