Robert is travelling on his cycle and has calculated to reach point A at 2…
2026
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
- A.
8 kmph
- B.
11 kmph
- C.
12 kmph
- D.
14 kmph
Attempted by 197 students.
Show answer & explanation
Correct answer: C
Key idea: the difference in travel times at two speeds gives the distance.
Let the distance be x km. Time at 10 km/h = x/10 hours; time at 15 km/h = x/15 hours. Their difference is 2 hours, so x/10 - x/15 = 2.
Solve: (3x - 2x)/30 = 2 ⇒ x/30 = 2 ⇒ x = 60 km.
Time to travel 60 km at 10 km/h is 60/10 = 6 hours, so if arrival is at 2:00 PM the start time must be 6 hours earlier: 8:00 AM.
To arrive at 1:00 PM starting at 8:00 AM he needs to travel for 5 hours. Required speed = distance/time = 60 km ÷ 5 h = 12 km/h.
Answer: 12 kmph