Dear Reader, Below are three distance-time problems involving trains.
Question 1
Hyderabad Chennai Express started from Hyderabad at 6 am. Chennai Hyderabad Express also started from Chennai at the same time. The first train was travelling at 40 km per hour and the second train was running at 55 km per hour. When the two trains met the first train had travelled 105 km less than the second train. What is the distance between Hyderabad and Chennai.
a) 665 km b) 705 km c) 725 km d) 740 km
Answer : a) 665 km
Solution :
Let both the trains meet after t hours since start.
Distance covered by I train in t hours = speed x time = 40t
Distance covered by II train in t hours = speed x time = 55t
When the trains cross each other the difference in distance is 105 Km (as given),
Therefore 55t - 40t = 105
15t = 105
or t = 7 hour ie the trains would cross each other in 7 hours.
In 7 hours, First train would had run -- 40 x 7 = 280 km
In 7 hours, the Second train would had covered -- 55 x 7 = 385 km
Distance between Hyderabad and Chennai = Sum of distances covered by both the trains in 7 hours = 280 + 385 = 665 km.
Question 2
Two Express trains – one from Mumbai to Bengaluru and another from Bengaluru to Mumbai started at the same time viz. 8 am. The first train was running at a speed of 60 km/hour and the second train was travelling faster than first train. Two trains cross each other at 7 hours from the start. If the distance between Bengaluru and Mumbai is 980 km, find the speed of the second train?
a) 80 kmph b) 90 kmph c) 70 kmph d) Can't be determined
Answer : a) 80 kmph
Solution :
In 7 hours the trains cross each other.
In 7 hours I train would had covered a distance of speed x time = 60 x 7 = 420 km
Let the speed of second train be s
In 7 hours, II train would had covered 7s km.
Distance between Bengaluru and Mumbai = 980 Km = Sum of the distances covered by both the trains
i.e 420 + 7s = 980
7s = 560
s = 80 kmph
Question 3
Mumbai Chennai Express (Train A) and Chennai Mumbai Express (Train B) started from Mumbai and Chennai stations respectively at 8 am. Train A was running at 65 km per hour and Train B was running at a greater speed than train A. Two trains meet each other after 9 hours. How you can express speed of Train B as a function of distance D between Mumbai and Chennai?
a) (D - 585/9) b) (D - 585) / 9 c) (D + 585) /9 d) can't be determined
Answer : b) (D - 585) / 9
Solution :
Trains cross each other after 9 hours.
Distance covered by Train A in 9 hours = 65 x 9 = 585
Let speed of train B be s
Distance covered by Train B in 9 hours = 9s
Let the distance between Mumbai and Chennai be D.
Distance between Mumbai and Chennai = D = Sum of distances covered by the trains in 9 hours = 585 + 9s
D = 585 + 9s
Or s = (D - 585) / 9