Question

Surekha Travels $ 10 $ km to reach her office. She walks $ 0.5 $ km on foot at a speed of $ 8 $ km to catch a bus which Travels at a speed of $ 40 $ km. What is the time taken by Surekha to reach the office?

Answer 1

Hint: Here we will use the concept of the speed which is the ratio of distance travelled by the time taken and then will frame the given data in the formula and simplify for the resultant required values to get the time taken by Surekha to reach the office.

Complete step-by-step answer:
Given that: total distance traveled to reach the office, $ D = 10 $ km
Considering the motion during the walk,
Speed of Surekha during walk, $ v = 8\dfrac{{km}}{h} $
Distance travelled during the walk, $ d = 0.5 $ km
Let us assume that the time spent during walk be “t” and it can be given as
 $ t = \dfrac{d}{v} $
Place the values in the above expression –
 $ t = \dfrac{{0.5}}{8} $
Simplify the above expression –
 $ t = 0.0625 $ h ….. (A)
Considering the motion during the travel by bus –
Speed of bus, $ V = 40\dfrac{{km}}{h} $
Distance remaining to travel to reach the office is given by the difference of the distances
 $ d' = 10 - 0.5 = 9.5 $ km
Let the time spent in travelling by bus, $ t' $
It is expressed as –
 $ t' = \dfrac{{d'}}{V} $
Place the values in the above equation –
 $ t' = \dfrac{{9.5}}{{40}} $
Simplify the above expression –
 $ t' = 0.2375 $ h ….. (B)
By using equations (A) and (B) -
Total time taken to reach office is given by –
 $ T = t + t' $
Place the values in the above equation –
 $ T = 0.0625 + 0.2375 $
Simplify by adding the terms in the above expression –
 $ T = 0.3h $
Convert hours in minutes –
 $ T = 0.3 \times 60 $
Simplify the above expression finding the product of the terms –
 $ T = 18 $ minutes
Hence, Surekha will take $ 18 $ minutes to reach the office.
So, the correct answer is “ $ T = 18 $ minutes”.

Note: Always remember the basic conversational relations between the different units of time. Know the relation between the hour, minutes and second and apply it accordingly. Always check the units of the given data and after that only place in the formula to simplify.