Question

Katya and Leena both live 3km from school.
(a) Katya walks to school at an average speed of \[5\dfrac{km}{hr}\] . She leaves home at 8 am. What time does she get to school?
(b) Leena 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: First, we will use the formula related to time, speed and distance which is given as \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\] . In case (a), simply using the formula we will find time. In case (b), we will first find the time difference between 8.30am and 8.10am. Using that time which will be in minutes, we will convert it in hours using the conversion \[\text{1hr=60minutes}\] and then using the same formula we will find average speed. Thus, we will get an answer.

Complete step-by-step answer:
Here, we will use the formula related to speed, time and distance given as \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\] .
Taking case (a): It is given that speed is \[5\dfrac{km}{hr}\] and distance is 3km. So, by using the formula \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\] , we will find the time. We get as
\[\text{5}\dfrac{km}{hr}\text{=}\dfrac{3km}{\text{time}}\]
On solving, we get as
\[time\text{=}\dfrac{3km}{\text{5}\dfrac{km}{hr}}\]
\[time\text{=0}\text{.6hr}\]
Now, we are told that Katya leaves home at 8 am. So, at what time she reaches school. For this we will convert time from hours to minutes using the conversion \[\text{1hr=60minutes}\] . So, using unitary method, we get as
\[\begin{align}
  & \text{1hr=60minutes} \\
 & \text{0}\text{.6hr=?} \\
\end{align}\]
On solving, we get as
\[\text{0}\text{.6 }\!\!\times\!\!\text{ 60=36minutes}\]
Thus, adding 36 minutes to 8 am, we get final time as 8hr 36minutes. ……………………………..(1)
Taking case (b): Here, we have to find average speed. Time at which Leena leaves for school is 8:10 am and reaches school at 8.30 am. So, the time difference will be \[8.30-8.10=0.20\] minutes. So, Here we will take the time as 20 minutes. Thus, we get using the formula \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\] is
\[\text{speed=}\dfrac{3km}{20\min }\]
But we want to calculate speed in km per hour, so we will convert minute to hour using the conversion rule \[\text{1hr=60minutes}\] . By unitary method, we get as
\[\begin{align}
  & \text{1hr=60minutes} \\
 & \text{?=20minutes} \\
\end{align}\]
On solving, we get as
\[\dfrac{20}{60}=\dfrac{1}{3}hr\]
So, putting this value in place of 20 minutes, we get equation as
\[speed=\dfrac{3km}{\dfrac{1}{3}hr}=\dfrac{3\times 3}{1}\dfrac{km}{hr}\]
\[speed=9\dfrac{km}{hr}\]
Thus, the average speed of Leena is \[9\dfrac{km}{hr}\] . …………..…….(2)
Hence, equation (1) and (2) are answers to case (a) and (b) respectively.

Note: Sometimes students make mistake in taking time i.e. let say in case (b) time should be taken as difference between timings but instead if taken as 8.30am i.e. 8 hour 30 minutes and using this if we put in formula \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\] , then speed will be totally difference which will be wrong. So, do not make this mistake.