Question

Katya and Teena both live 3 km from the school.
A. Katya walks to school at an average speed of 5 km/hr. She leaves home at 8 am. What time does she get to school?
B. Teena cycles to school. She leaves home at 8 : 10 am and reaches school at 8 : 30 am. What is her average speed?

Answer 1

Hint: To solve the question given above, we will first find out what is the meaning of average speed. Then we will solve each part that is given in the question separately. To solve the first part, we will apply the formula of average speed that is given by, $\text{average speed}=\dfrac{\text{total distance travelled}}{\text{total time taken}}$. From here, we will get the total time and then we will add this to 8 am to get the reaching time. After this we will apply the formula of average speed to get the final answer.

Complete step-by-step answer:
Before we solve the question given above, we must know what is average speed. The average speed of an object is the total distance travelled by the object divided by the elapsed time to cover that distance. Now, we are given two parts in the question, so we will solve each part separately.
A. In this part, we have to find the time at which Katya gets to school. So, for this we will find the total time taken by her to reach the school. Now, we know that $\text{average speed}=\dfrac{\text{total distance travelled}}{\text{total time taken}}$. In our case here, the average speed is 5 km/hr and the total distance is 3 km. Thus, we have,
$\begin{align}
  & 5km/hr=\dfrac{3km}{\text{total time}} \\
 & \Rightarrow \text{total time}=\dfrac{3}{5}hr \\
\end{align}$
We know that, in 1 hour, there are 60 minutes, so we will get,
$\begin{align}
  & \text{Total time}=\dfrac{3}{5}\times 60\text{ minutes} \\
 & \Rightarrow \text{Total time}=36\text{ minutes} \\
\end{align}$
So, now Katya will reach the school at (8 : 00 + 36 minutes). Therefore, Katya will reach the school at 8 : 36 am.
B. In this part, we will first find the total time taken by Teena to reach school. Now, Teena leaves at 8 : 10 am and reaches at 8 : 30 am. Thus, the total time taken by her is 20 minutes. Now, in one hour there are 60 minutes, so, we can say that,
$\begin{align}
  & 1\text{ hour}=60\text{ minutes} \\
 & 1\text{ hour}=3\times 20\text{ minutes} \\
 & \Rightarrow 20\text{ minutes}=\dfrac{1}{3}\text{ hour} \\
\end{align}$
Now, we will apply the formula of average speed, $\text{average speed}=\dfrac{\text{total distance travelled}}{\text{total time taken}}$. So, we get,
$\begin{align}
  & \text{Average speed}=\dfrac{3km}{\left( \dfrac{1}{3} \right)hour} \\
 & \Rightarrow \text{Average speed}=9km/hr \\
\end{align}$
Thus, the average speed of Teena is 9 km/hr.

Note: In part B, we are not given in which unit, we have to find the average speed. We have found the speed in kilometres per hour unit. We can also change the unit to metre per second unit as shown below.
$\begin{align}
  & \text{Average speed}=9km/hr \\
 & \Rightarrow \text{Average speed}=\dfrac{9\times 1000\text{ metres}}{60\times 60\text{ seconds}} \\
 & \Rightarrow \text{Average speed}=\dfrac{90}{36}\text{ m}/\sec \\
 & \Rightarrow \text{Average speed}=\dfrac{5}{2}\text{ m}/\sec \\
 & \Rightarrow \text{Average speed}=2.5\text{ m}/\sec \\
\end{align}$