Real-life Problems Based on Speed, Time and Distance: Formulas, Examples

When children or regular people apply mathematics to address Real-life Problems Based on Speed, Time and Distance, they learn that math is more than a task to accomplish for the purpose of the teacher. It also gives children vital skills for influencing their surroundings. The speed of a moving object is defined as the distance it travels in one unit of time. This article will teach us about the mathematical link between speed, distance, and time.

Although the concepts of speed, time, and distance remain the same, the types of questions presented in tests may vary. One of the most common quantitative aptitude topics asked in government tests are speed, time, and distance. This is one of those topics that students are already aware of before they begin studying for competitive exams.

It is essential for students to learn the concept of Speed, Time and Distance. With regular practice of problems, they can develop speed which will, in turn, help them score higher marks in the exam. Continue reading to know more.

Speed

The word speed refers to how quickly something or someone is moving. If we know the distance traveled and the time it took, we may estimate an object’s average speed. The rate at which an object travels is known as speed (covering a particular distance). It’s a scalar quantity because it only defines magnitude, not direction.

The formula used to find the speed is given by,

The meter per second \((\rm{m/s})\) is the SI unit for speed.

Example:

From the above example, as the speed increases, the time decreases.

Learn Formulas for Speed Time Distance

Time

Time is a measured duration during which an action or event occurs. The time formula calculates how long an object takes to travel a certain distance at a given speed.

Seconds is the SI unit for time \((\rm{s}).\)

Distance

The length of the line segment that connects two points is called distance. The distance is the extent or amount of space between two things, points, lines, etc.

Meter is the SI unit for distance.

Relation of Speed, Time, and Distance

Now, we shall look at the mathematical relation between speed, distance, and time. The speed of a moving body is the distance it travels in a unit amount of time.

\({\text{Speed = }}\frac{{{\text{distance}}}}{{{\text{time}}}}\)

If the distance is in kilometers and the time is in hours, the speed is in kilometers per hour.
The speed is \(\rm{m/sec}\) if the distance is measured in metres and the time is measured in seconds.

\({\rm{Distance}} = {\rm{speed}} \times {\rm{time}}\)

Meter is the SI unit for distance.

\({\text{Time = }}\frac{{{\text{distance}}}}{{{\text{speed}}}}\)

Seconds is the SI unit for time \((\rm{s}).\)

When the distance is constant, speed is inversely proportional to time. When \(D\) is constant, \(S\) is inversely proportional to \(T\).
The time taken will be in the ratio \(n : m\) if the speeds are \(m : n.\)

When the distance traveled remains constant, speed is inversely related to the time required. As a result, as speed rises, time decreases, and vice versa.

Formulas of Speed, Distance and Time

All fundamental problems can be solved using these formulas. When applying the given formulas, you should ensure that the units are used correctly. When the distance traveled remains constant, speed is inversely related to the time required. As a result, as speed rises, time decreases, and vice versa.

Units of Speed, Distance and Time

Time: seconds \((\rm{s})\), minutes \((\rm{min})\), hours \((\rm{hr})\)
Distance: metres \((\rm{m})\), kilometres \((\rm{km})\), miles, feet
Speed: \({\rm{m/s}},\,{\rm{km/hr}}.\) If the distance is in \({\rm{km}}\) and the time is in \({\rm{hr}}\), then \({\text{Speed = }}\frac{{{\text{distance}}}}{{{\text{time}}}}\) and the unit of speed will be \(\rm{km/hr}.\)

Effect of Speed and Time on Distance

Understand that whatever speed we choose involves both distance and time. “Faster” can mean “far” (a greater distance) or “quicker” (a shorter distance) (less time). To double one’s travel distance at the same time, one must increase their speed. When one’s speed increases, it takes to cover the same distance is cut in half. Distance is unchanged by speed. It can affect the time it takes to cover or cross a certain distance.

Real-Life Problems Based on Speed, Time and Distance

1. A boy walks at a speed of \(5\,\rm{kmph}\). How much time does he take to walk \(20\,\rm{km}\)?
We know, \({\text{Time = }}\frac{{{\text{distance}}}}{{{\text{speed}}}}\)
So, the time required to walk \( = \frac {20}{5} = 4\,\rm{hours}\)
So, the boy walks \(20\,\rm{km}\) in \(4\,\rm{hours}\).

2. A cyclist covers \(14\,\rm{miles}\) in \(2\,\rm{hours}\). Calculate his speed.
We know, \({\text{Speed = }}\frac{{{\text{distance}}}}{{{\text{time}}}}\)
Hence, the \({\text{Speed}} = \frac{14}{2} = 7\,{\text{miles}}\,{\text{per}}\,{\text{hour}}.\)
So, the speed of cyclists is \(7\,{\text{miles}}\,{\text{per}}\,{\text{hour}}.\)

3. A cyclist travels at a speed of \(25\,\rm{km/hour}\). How far will he travel in \(50\,\rm{minutes}\)?
We know, \({\rm{Distance}} = {\rm{speed}} \times {\rm{time}}\)
So, the distance travelled in \(50\) minutes \(25 \times \frac{{50}}{{60}} = 20.83\,{\text{km}}\)
So, the cyclist travels \(20.83\,{\text{km}}.\)

Solved Examples – Real Life Problems Based on Speed, Time and Distance

Q.1. A car travels \(320\,\rm{km}\) in \(4\,\rm{hours}.\) What is its speed in \(\rm{km/hr}\)?
Ans: We know the formula for speed is given by, \({\text{Speed = }}\frac{{{\text{distance}}}}{{{\text{time}}}}\)
\( \Rightarrow {\text{speed}} = \frac{{320}}{4} = 80\,{\text{km/hr}}.\)
Therefore, the speed at which a car travels is \(80\,{\text{km/hr}}.\)

Q.2. Traveling at a speed of \(45\,\rm{kmph}\), how long will it take to travel \(135\,\rm{km}\)?
Ans: Given, speed \(= 45\,{\text{kmph}}\), distance \(= 135\,{\text{km}}\)
We know the relation between speed distance and time is, \({\text{speed}} = \frac{{{\text{distance}}}}{{{\text{time}}}}\)
\( \Rightarrow 45\,{\text{kmph}} = \frac{{135\,{\text{km}}}}{{{\text{time}}}}\)
\( \Rightarrow {\text{time}} = \frac{{135\,{\text{km}}}}{{45\,{\text{kmph}}}}\)
\( = 3\,{\text{hours}}\)
Therefore, the required time to complete \(135\,{\text{km}}\) is \( 3\,{\text{hours}}.\)

Q.3. A truck was running from a city at an initial speed of \(40\,\rm{kmph}\). The truck’s speed was increased by \(3\,\rm{kmph}\) at the end of every hour. Find the total distance covered by the truck in the first \(5\,\rm{hours}\)  of the journey.
Ans: The total distance covered by the truck in the first \(5\,\rm{hours}\)
\(= 40 + 43 + 46 + 49 + 52\)
\(= 230\,\rm{kms}\)
Therefore, \(230\,\rm{km}\) is the total distance covered by the truck in the first \(5\,\rm{hours}\) of the journey.

Q.4. Arun can run a distance of \(120\,\rm{m}\) in \(20\,\rm{seconds}\). Find the speed of Arun in \(\rm{m/s}.\)
Ans: Given, time \(= 20\,\rm{seconds}\), distance \(= 120\,\rm{m}\), speed \(=\)?
We know, \({\text{speed = }}\frac{{{\text{distance}}}}{{{\text{time}}}}\)
\( \Rightarrow {\text{speed}} = \frac{{120}}{{20}} = 60\,{\text{m}}/{\text{s}}\)
Hence, the speed of Arun is \(60\,{\text{m}}/{\text{s}}.\)

Q.5: Travelling at a speed of \(50\,\rm{kmph}\), how long will it take to travel \(80\,\rm{km}\)?
Ans: Given, speed \(= 50\,\rm{kmph}\), distance \(= 80\,\rm{km}\)
We know the relation between speed distance and time is \({\text{time = }}\frac{{{\text{distance}}}}{{{\text{speed}}}}\)
\( \Rightarrow {\text{time}} = \frac {{80}}{{50}}\)
\( \Rightarrow {\text{time}} = \frac {{8}}{{5}}\)
\( \Rightarrow {\text{time}} = 1.6\;\rm{hours}\)
\( \Rightarrow {\text{time}} = 1\,{\rm{hour}}\,36\,{\rm{minutes}}\)
Therefore, \(1\,{\rm{hour}}\,36\,{\rm{minutes}}\) is going to take to travel \(80\,\rm{km}.\)

Q.6. If the distance travelled by train is \(405\,\rm{km}\) in \(4\,{\rm{hours}}\,30\,{\rm{minutes}}\), what is its speed?
Ans: Given, time \(= 4\,{\rm{hours}}\,30\,{\rm{minutes}} = 4.5\,{\rm{hours}}\),distance \(= 500\,\rm{km}\),speed \(=\)?
We know, \({\text{speed}} = \frac{{{\text{distance}}}}{{{\text{time}}}}\)
\( \Rightarrow {\text{speed}} = \frac{{405}}{{4.5}}\)
\( \Rightarrow {\text{speed}} = 90\,{\text{km}}/{\text{hr}}\)
Hence, the obtained speed is \(90\,{\text{km}}/{\text{hr}}.\)

Q.7. Express the speed of \(90\,\rm{meters}\) per minute in kilometres per hour.
Ans: Given, speed \( = 90\,{\text{meters}}/{\text{minutes}}\)
We know \(1\,{\text{meter}} = \frac{1}{{1000}}\;{\text{km}}\) and \(1\,{\text{minute}} = \frac{1}{{60}}{\text{hour}}\)
Hence, the speed \(= 90 \times \frac{{\frac{1}{{1000}}{\text{km}}}}{{\frac{1}{{60}}\;{\text{hr}}}}\)
\( \Rightarrow {\text{speed}} = 90 \times \frac{{60}}{{1000}}\)
\( \Rightarrow {\text{speed}} = 9 \times \frac{6}{{10}}\)
\( \Rightarrow {\text{speed}} = \frac{{54}}{{10}}\)
\( \Rightarrow {\text{speed}} = 5.4\,{\text{km}}/{\text{hr}}\)
Therefore, the speed can be expressed as \(5.4\,{\text{km}}/{\text{hr}}.\)

Q.8. A car travels a distance of \(600\,{\text{km}}\) in \(10\,{\rm{hours}}\). What is its speed?
Ans: Given, time \(= 10\,\rm{hours}\), distance \(= 600\,\rm{km}\), speed \(=\)?
We know that \({\text{speed}} = \frac{{{\text{distance}}}}{{{\text{time}}}}\)
\(\Rightarrow {\text{speed}} = \frac{{600}}{{10}}\)
\( \Rightarrow {\text{speed}} = 60\,{\text{km}}/{\text{hr}}\)
Therefore, the obtained speed is \(60\,{\text{km}}/{\text{hr}}.\)

Summary

This article includes the definition of speed, distance and time, the relationship among those three formulas. It helps to solve various problems, including real-life problems, too quickly. This article helps better understand “Real Life Problems Based on Speed, Time and Distance”. This article’s outcome helps in applying the suitable formulas while solving the various problems based on them.

Solve Important Problems on Trains

Frequently Asked Questions (FAQs)

We have provided some frequently asked questions here:

Q.1. What is the formula for speed and distance?
Ans: The formula to find speed is given by, \({\text{speed}} = \frac{{{\text{distance}}}}{{{\text{time}}}}\)
The formula to find the distance is given by, \({\text{distance}} = {\text{speed}} \times {\text{time}}.\)

Q.2. What is the difference between speed and distance?
Ans: The rate at which the distance is travelled in unit time is referred to as the speed. The speed is equal to \(S = \frac{D}{T}\) if ‘\(D\)’ is the distance travelled by an item in time ‘\(T\)’.

Q.3. What is the effect of speed and time on distance?
Ans: Whatever speed we choose, understand that it involves both distance and time. Increasing one’s speed involves increasing one’s travel distance in the same amount of time. Increasing one’s speed also cuts the time it takes to cover the same distance.

Q.4. How do you solve problems involving speed, distance and time?
Ans: Speed is calculated using the formula \({\text{speed}} = \frac{{{\text{distance}}}}{{{\text{time}}}}.\) We need to know the units for distance and time to figure out the units for speed. Because the distance is measured in metres \((\rm{m})\) and the time is measured in seconds \((\rm{s})\), the units will be metres per second \((\rm{m/s}).\)

Q.5. How do you find speed and distance in a math problem?
Ans: Speed and distance can be calculated by using the formula,
\({\text{speed}} = \frac{{{\text{distance}}}}{{{\text{time}}}}\)
The formula to find the distance is given by, \({\text{distance}} = {\text{speed}} \times {\text{time}}.\)

Q.6. What is the mathematical relationship between speed, distance and time?
Ans: The mathematical relation between speed, distance, and time is that in a moving body, the speed is the distance it travels in a unit amount of time.
If the distance is in kilometres and the time is in hours, the speed is in kilometres per hour.
The speed is \(\frac{{\text{m}}}{{{\text{sec}}}}\), if the distance is measured in metres and the time is measured in seconds.

We hope this detailed article on some real-life problems based on speed, distance and time helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!