A girl goes to her college which is 100 km away. She goes to college…
2025
A girl goes to her college which is 100 km away. She goes to college travelling few distance by bicycle and remaining by train. The speed of bicycle is 24 kmph and that of train is twice of the bicycle. If she spend 40 minutes more on bicycle, then total time taken by her to go to college?
- A.
1 hour 10 min
- B.
2 hour 20 min
- C.
1 hour 50 min
- D.
3 hours
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Time = Distance / Speed. When a journey is split across two segments travelled at different constant speeds, and the two segment-times differ by a stated amount, express one segment's time using a variable, write the other segment's time in terms of it using that stated difference, then use the fact that the two segment-distances add up to the given total distance to form one linear equation in that variable.
Speed of bicycle = 24 km/h; speed of train = 2 x 24 = 48 km/h.
Let the time taken by train be t hours. Since she spends 40 minutes (2/3 hour) more on the bicycle, time taken by bicycle = (t + 2/3) hours.
Distance covered by train = 48t km; distance covered by bicycle = 24(t + 2/3) km.
Total distance is 100 km, so: 48t + 24(t + 2/3) = 100.
Expanding: 48t + 24t + 16 = 100, so 72t = 84, giving t = 84/72 = 7/6 hours.
Total time = time by train + time by bicycle = t + (t + 2/3) = 2t + 2/3 = 2 x (7/6) + 2/3 = 14/6 + 4/6 = 18/6 = 3 hours.
Check: train covers 48 x 7/6 = 56 km; bicycle time is 7/6 + 2/3 = 11/6 hours, so bicycle covers 24 x 11/6 = 44 km. Together, 56 + 44 = 100 km, matching the given total distance, and the two times sum to 7/6 + 11/6 = 18/6 = 3 hours.
So the total time taken by her to travel to college is 3 hours.