A mini-van crosses two people walking at the speed of 4.8 km/h and 6 km/h in the same direction as that in which the mini-van is heading in 4.5 s and 9 s, respectively. What is the length of the mini-van?

# Given-

v1 = 4.8 km/hr

v2 = 6 km/hr

$$t1 = 4.5 s = \frac{1}{800} hr$$   {$$1s=\frac{1}{60\times60}h$$}

  # Solution-

Let x km be length of the minivan and y km/hr be its speed.

$$time=\frac{distance}{speed} $$

In same direction 

Y -v1

Y-v2

Applying given conditions -

$$\frac{x} { (y-4.8)} =\frac{1}{800} $$

800x = y-4.8 ...(1)

$$\frac{x} { (y-6)} =\frac{1}{400} $$

400x = y-6 ...(2)

Eqn.(1) - eqn.(2)

800x - 400x = y-4.8 -y+6

400x = 1.2

$$x = \frac{1.2}{400}$$

$$x = 3\times10^{-3}$$

x = 3 m

Therefore, length of the minivan is 3 m.