If I walk with 30 km/hr , I reach 1 hour before and if I walk with 20 km/hr I…

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If I walk with 30 km/hr , I reach 1 hour before and if I walk with 20 km/hr I reach 1 hour late. Find the distance between two points and the exact time of reaching destination is 11 am then find the speed with which it walks .

  1. A.

    120 km and 25 km/hr

  2. B.

    144 km and 24 km/hr

  3. C.

    120 km and 24 km/hr

  4. D.

    150 km and 25 km/hr

Attempted by 37 students.

Show answer & explanation

Correct answer: C

Let d be the distance (in km) and t be the scheduled travel time (in hours) at the usual speed.

  • If the speed is 30 km/hr, the traveller arrives 1 hour early, so time taken = t - 1 and d = 30(t - 1).

  • If the speed is 20 km/hr, the traveller arrives 1 hour late, so time taken = t + 1 and d = 20(t + 1).

  • Equate the two expressions for d: 30(t - 1) = 20(t + 1).

  • Solve: 30t - 30 = 20t + 20 ⇒ 10t = 50 ⇒ t = 5 hours.

  • Distance: d = 30(t - 1) = 30*(5 - 1) = 120 km.

  • Usual speed: d / t = 120 / 5 = 24 km/hr.

  • If the arrival time is 11:00 AM, then the start time = 11:00 AM − 5 hours = 6:00 AM.

Answer: Distance = 120 km; usual speed = 24 km/hr. (Departure at 6:00 AM if arrival is 11:00 AM.)

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