Question

Monika takes \[\dfrac{1}{6}\] hour to walk to the playground and \[\dfrac{1}{3}\] hour to walk from the playground to school. How much time does it take her to walk to the playground and then to school?
A. \[\dfrac{2}{9}\] hour
B. \[\dfrac{1}{3}\] hour
C. \[\dfrac{1}{2}\] hour
D. \[\dfrac{2}{3}\] hour

Answer 1

Hint: As we can see that it takes Monika \[\dfrac{1}{6}\] hour to walk to the playground from her initial position, and it takes \[\dfrac{1}{3}\] hour to walk from the playground to the school. Now for Monika to reach her school first she has to go to the playground and then she will travel to her school from the playground.

Complete step-by-step answer:
It is given to us that the time taken by Monika to travel from her current position to playground is –
\[{{T}_{IP}}=\dfrac{1}{6}\] hour, where I – Initial position, P – Playground
It is given to us that the time taken by Monika to travel from playground to school is –
\[{{T}_{PS}}=\dfrac{1}{3}\] hour, where P – Playground, S – School
It is also necessary to note that while travelling from current position to the school, she will definitely encounter the playground, which means that first she will reach the playground and then from there she will travel to reach the school. This means that time taken during the whole journey will be a sum of time taken by her to reach the playground and time taken by her to travel from playground to the school.
Time taken by her to travel from current position to her school = Time taken by her to reach the playground from her position + Time taken by her to travel from playground to the school
\[{{T}_{IS}}={{T}_{IP}}+{{T}_{PS}}\]
\[{{T}_{IS}}=\dfrac{1}{6}+\dfrac{1}{3}\]
\[{{T}_{IS}}=\dfrac{1+2}{6}\]
\[{{T}_{IS}}=\dfrac{1}{2}\] hour, where I – Initial position, S – School
Given that the answer is \[\dfrac{1}{2}\] hour our correct option is C

Note: The student must be familiar with the concept of addition of ratios, change of units, etc. The common mistakes are that students sometimes add time with different units which must be avoided because it gives wrong answers, Taking wrong LCM in the denominator, inability to remember conversion factor of units.