Samuel covers the distance from his home to his office at a speed of 25 km/hr…

2023

Samuel covers the distance from his home to his office at a speed of 25 km/hr and comes back at a speed of 4 km/hr. He completes the whole journey within 5 hours 48 minutes. Find out the distance from his home to office:

  1. A.

    20 km

  2. B.

    18 km

  3. C.

    15 km

  4. D.

    25 km

Attempted by 43 students.

Show answer & explanation

Correct answer: A

Answer: 20 km

Explanation:

  1. Let d be the one-way distance from home to office (in km).

  2. Time to go = d/25 hours. Time to return = d/4 hours. So total time = d/25 + d/4.

  3. Compute the sum: d/25 + d/4 = d*(1/25 + 1/4) = d*(4+25)/100 = 29d/100.

  4. Given total time is 5 hours 48 minutes = 5 + 48/60 = 5.8 = 29/5 hours. Set 29d/100 = 29/5.

  5. Solve for d: 29d/100 = 29/5 ⇒ d = (29/5) × (100/29) = 20 km.

  6. Therefore, the distance from his home to office is 20 km.

Alternate method (harmonic mean): average speed for the round trip = (2×25×4)/(25+4) = 200/29 km/h. Total distance = average speed × total time = (200/29)×(29/5) = 40 km, so one-way distance = 40/2 = 20 km.

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