Questions & Answers: "Variation, Time and Work"

To pass a tunnel, the train must cover a distance equal to its own length plus the length of the tunnel.The total distance ($D$) to be covered is the sum of the length of the train ($L_T$) and the length of the tunnel ($L_{Tunnel}$):$D = L_T + L_{Tunnel} = 1000\text{ m} + 800\text{ m} = 1800\text{ m}$The speed of the train ($S_T$) is given as $72$ km/hr. We need to convert this speed to meters per second (m/s):$S_T = 72\text{ km/hr} = 72 \times \frac{1000\text{ m}}{3600\text{ s}} = 72 \times \frac{5}{18}\text{ m/s} = 4 \times 5\text{ m/s} = 20\text{ m/s}$Now, we can calculate the time ($T$) taken using the formula $T = \frac{D}{S_T}$:$T = \frac{1800\text{ m}}{20\text{ m/s}} = 90\text{ seconds}$We also need to check the options in minutes. $90$ seconds is equal to $\frac{90}{60}$ minutes, which is $1.5$ minutes or $1\frac{1}{2}$ minutes.Therefore, both $90$ seconds and $1\frac{1}{2}$ minutes are correct alternatives.