Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q…

2023

Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q at 8 a.m. at the speed of 25 km/hr. Another rider starts from Q towards P at 9 a.m. at the speed of 20 km/hr. Find at what time they will cross each other?

  1. A.

    2.45 p.m

  2. B.

    2.30 p.m.

  3. C.

    1.35 p.m.

  4. D.

    1.15 p.m.

Attempted by 2 students.

Show answer & explanation

Correct answer: B

Initial Setup: The two towns, P and Q, are 275 km apart. The first rider starts from P at 8 a.m. at 25 km/hr. The second rider starts from Q at 9 a.m. at 20 km/hr.

  • Methodology: Relative speed for two bodies moving in opposite directions is the sum of their individual speeds (SR = S1 + S2).

  • Calculation:

    • Let the distance traveled by the first rider be 25 * x km.

    • Let the distance traveled by the second rider be 20 * (x - 1) km.

    • Setting up the equation for the total distance: 25x + 20(x - 1) = 275.

    • Solving this gives x = 6.5 hours.

    • The second rider travels for x - 1, which equals 5.5 hours.

  • Final Result: The riders cross each other 5.5 hours after 9 a.m., which is 2:30 p.m..

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