If Tanya walks at the speed of 6 km/h, she misses a train by 2 minutes. However, if she walks at the speed of 8 km/h, she reaches the station 3 minutes before the arrival of the train. The distance covered by Tanya to reach the station is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 2 km.
Let the distance to the station be 'd' kilometers.
⇒ The difference in time between the two walking speeds is 2 minutes (missing) + 3 minutes (early) = 5 minutes.
⇒ Time at 6 km/h: Time = Distance / Speed = d / 6 hours
⇒ Time at 8 km/h: Time = Distance / Speed = d / 8 hours
⇒ 5 minutes = 5/60 hours = 1/12 hours
⇒ Since Tanya takes 1/12 hour less time at 8 km/h:
⇒ (d / 6) - (d / 8) = 1/12
⇒ (24): (4d / 24) - (3d / 24) = 2/24
⇒ d / 24 = 2/24
⇒ d = 2 kilometers
Therefore, the distance covered by Tanya to reach the station is 2 kilometers.