Question

Two towns T₁ and T₂ are connected by regular bus service. A scooterist moving from T₁ to T₂ speed of 20 kmh^-1 notices that a bus goes past it every 21 minute in the direction of his motion and every 7 minute in the opposite direction. If a bus leaves in either direction every 1 minute, the period t is

• A. 1.5 minute
• B. 9.5 minute
• C. 6 minute
• D. 10.5 minute

Answer 1

Answer: (B)

9.5 minute

Answer 2

But (say B1) in the same direction relative speed of bus and cyclist,

v_r = v_b – v_c Distance traveled by B1 relative of cyclist in 21 minutes = v_r × 21

Distance covered by bus in T minute = vbT

Then 21 v_r = v_b + T

But in the opposite direction (say B₂)

Relative speed between B₂ and cyclist,

v_r = v_b + v_c

Distance traveled by B2 relative to cyclist in 7 minutes = vr × 7

Then 7v_r = v_b T

Frp, (i) and (ii)

21 v_r = 7v_r or 3v_r = v_r or 3(v_b - v_c) = v_b + v_c or v_b = 2v_c = 2 × 20 = 40 kmh^-1

Thus T = $\frac{7v_{r}}{v_{b}} = \frac{7\left( v_{b} + v_{c} \right)}{v_{b}} = \frac{7(40 + 20)}{40} = \frac{7 \times 3}{2}$ = $\frac{21}{2}$ = 10.5 minute