Question

Anuj takes 15 minutes to go to school and takes 20 minutes to come back from school by bicycle. If the school is 4.5 km away from his home, find his average speed.

Answer 1

Hint:Use the formula of speed to find the speed of Anuj to go to school and speed of return journey. We know speed is distance by time. Find both speed and then find average time.
Distance of the school from home
\[=4.5km=4.5\times 1000m=4500m\]
\[\because 1km=1000m\], convert km to m.

Complete step-by-step answer:
Time taken by Anuj to go from home to school = 15 minutes = \[{}^{15}/{}_{60}\] hour.
Time taken by Anuj to come back from school to home = 20 minutes = \[{}^{20}/{}_{60}\] hour.
We know the basic formula, \[Speed=\dfrac{distance}{time}\]
We have been given the distance and time. We need to find the speed.
Speed of Anuj from home to school \[=\dfrac{distance}{time}=\dfrac{km}{hr}=\dfrac{4.5}{{}^{15}/{}_{60}}=\dfrac{4.5\times 60}{15}=4.5\times 4=18{}^{km}/{}_{hr}.\]
Similarly speed of Anuj on return to home \[=\dfrac{distance}{time}=\dfrac{km}{hr}=\dfrac{4.5}{{}^{20}/{}_{60}}=\dfrac{4.5\times 60}{20}=4.5\times 3=13.5{}^{km}/{}_{hr}.\]
Thus we found out the two speeds as \[18{}^{km}/{}_{hr}\] and \[13.5{}^{km}/{}_{hr}\].
Now we need to find the average speed.
\[Average\text{ }Speed=\dfrac{Total\text{ }distance}{Total\text{ }time\text{ }taken}\]
Total distance travelled by Anuj = distance from home to school + distance from school to home
 = 4.5 + 4.5 = 9 km.
\[\begin{align}
  & Total\text{ }time\text{ }taken=\dfrac{distance}{speed} \\
 & \therefore time\text{ }taken=\dfrac{4.5}{18}={{t}_{1}} \\
 & \\
\end{align}\]
Time taken on return, \[{{t}_{2}}=\dfrac{4.5}{13.5}\]
\[\begin{align}
  & \therefore Average\text{ }speed=\dfrac{Total\text{ }distance}{Total\text{ }time\text{ }taken}=\dfrac{4.5+4.5}{{{t}_{1}}+{{t}_{2}}}=\dfrac{4.5+4.5}{\dfrac{4.5}{18}+\dfrac{4.5}{13.5}} \\
 & =\dfrac{4.5(1+1)}{4.5\left[ \dfrac{1}{18}+\dfrac{1}{13.5} \right]}=\dfrac{2\times 18\times 13.5}{13.5+18}=\dfrac{486}{31.5}=15.43{}^{km}/{}_{hr}. \\
\end{align}\]
Hence we got the average speed as \[15.43{}^{km}/{}_{hr}.\]

Note:You can also take the time taken as, \[{{t}_{1}}=\dfrac{15}{60}hr\] and \[{{t}_{2}}=\dfrac{20}{60}hr\].
Convert the minutes given into hours for time taken
We know 1 hour = 60 minutes and 1 minute = 60 seconds.
Thus, to convert minutes to hours, divide the minutes with 1 hour.
\[\therefore 15\min =\dfrac{15}{1hr}=\dfrac{15}{60}=\dfrac{1}{4}hour.\]