Question

A fast train covers 360 km in 3 hours 20 minutes. How much time will it take to cover a distance of 90 km?

Answer 1

Hint: Given that a fast train covers 360 km in 3 hours 20 minutes. Speed is calculated as distance/time which gives distance=speed × time and time is distance/speed. Distance and time are given so calculate the speed of the train. Using the obtained speed and distance 90km given, find the time it would take by the train to cover 90 km.

Complete step-by-step answer:
We are given that a fast train covers 360 km in 3 hours 20 minutes.
We have to calculate the time it will take to cover a distance of 90 km.
Speed is the ratio of total distance travelled to the time taken to travel this distance.
Train travels 360 km in 3 hours 20 minutes.
1 hour will have 60 minutes.
3 hours will have $ 3 \times 60 = 180 $ minutes.
3 hours 20 minutes will have $ 180 + 20 = 200 $ minutes.
Therefore, the train travels 360 km in 200 minutes.
  $
  speed = \dfrac{{dist}}{{time}} \\
  dist = 360km,time = 200\min \\
   \Rightarrow speed = \dfrac{{360}}{{200}} \\
   \Rightarrow speed = \dfrac{9}{5}km/\min \\
   $
Train travels 90 km and we have to calculate the time taken by the train to travel 90 km.
  $
  time = \dfrac{{dist}}{{speed}} \\
  speed = \dfrac{9}{5}km/\min ,dist = 90km \\
   \Rightarrow time = \dfrac{{90}}{{\left( {\dfrac{9}{5}} \right)}} = 90 \times \dfrac{5}{9} = 10 \times 5 \\
   \Rightarrow time = 50\min \\
   $
Therefore, the fast train takes 50 min to cover a distance of 90 km.

Note: One kilometre is equal to 1000 metres; one hour is equal to 60 minutes and one minute is equal to 60 seconds. Use this information to convert kilometres into metres, hours into minutes, minutes into seconds and vice-versa. Speed is the ratio of distance and time. Distance can be changed and time can be changed, but the ratio of distance and time should always be the same, which means the speed does not change for an object in uniform motion.