Multiple choice

A bus crosses a man with the speed of 54km/h. the length of the bus is 72 meter. After 10 seconds the man starts his car and ride in the direction of bus moving with the speed of 72 km/h. Find the distance travel by car when it covers the (\frac{2}{6})th length of the bus?

  1. 486 meter

  2. 525 meter

  3. 556 meter

  4. 696 meter

  5. None of these

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Bus speed = 54 km/h = 15 m/s. Bus length = 72 m. Bus covers 72 m in 72/15 = 4.8 seconds. After 10 seconds, man starts car. Bus has already traveled 10 × 15 = 150 m. Car speed = 72 km/h = 20 m/s. Car needs to cover (2/6) × 72 = 24 m relative to bus. Relative speed = 20 - 15 = 5 m/s. Time = 24/5 = 4.8 seconds. Car distance = 4.8 × 20 = 96 m. Total car travel when it reaches 2/6 of bus from start point: At car start, bus is at 150 m. Car needs to reach bus at 150 + 24 = 174 m from origin. Car travels 174 - (150 at car start from origin) + 150 (car start distance from origin) = 324 m... Wait, let me recalculate: Bus origin at t=0. At t=10, bus at 150m, car starts. Car needs to be at position where bus is + 24m from bus nose. At car start, bus nose at 150m. Car needs to reach 150+24 = 174m from origin. Car travels 174m in 174/20 = 8.7 seconds. In 8.7s, bus travels 8.7 × 15 = 130.5m. Bus position = 150 + 130.5 = 280.5m. That doesn't work. The 2/6 is 1/3 of bus length = 24m. When car has covered 24m relative to bus, car is at bus position + 24m. Let t be time after car starts. Car position = 20t. Bus position = 150 + 15t. Car is 24m ahead of bus: 20t = 150 + 15t + 24, 5t = 174, t = 34.8 seconds. Car distance = 20 × 34.8 = 696m.