Tim and Allen are 90 km from each other . They start to move each other…
2024
Tim and Allen are 90 km from each other . They start to move each other simultaneously . Tim at speed 10 and Allen 5 kmph . If every hour they double their speed what is the distance that Allen will pass until he meet Tim in km?
- A.
30
- B.
45
- C.
56
- D.
55
Attempted by 293 students.
Show answer & explanation
Correct answer: A
Answer: 30 km
Approach: Treat motion in hourly intervals. Each hour both speeds double at the end of the hour, so compute distances covered in each interval until they meet.
First hour: Tim speed = 10 km/h → distance = 10 km; Allen speed = 5 km/h → distance = 5 km. Combined = 15 km. Remaining distance = 90 - 15 = 75 km.
Second hour: speeds double to Tim = 20 km/h and Allen = 10 km/h. Distances this hour: Tim 20 km, Allen 10 km. Combined this hour = 30 km. Cumulative combined = 15 + 30 = 45 km. Remaining distance = 90 - 45 = 45 km.
Third interval: speeds double again to Tim = 40 km/h and Allen = 20 km/h. Relative speed towards each other = 40 + 20 = 60 km/h. Time to cover remaining 45 km = 45 / 60 = 3/4 hour.
Distance Allen covers in that final 3/4 hour = 20 × 3/4 = 15 km.
Total distance Allen covers until meeting = 5 (first hour) + 10 (second hour) + 15 (final part) = 30 km.