A train travelling at a speed of 60 km\/hr crosses a platform in 20 seconds. The same train crosses a person who is walking at a speed of 6 km\/hr in the same direction as that of the train in 12 seconds. What is the length of the train and that of the platform, respectively ?<\/p>\n
[amp_mcq option1=”160 m and 153.33 m” option2=”170 m and 166.66 m” option3=”180 m and 153.33 m” option4=”180 m and 170 m” correct=”option3″]<\/p>\n
Case 1: Train crosses a platform in 20 seconds.
\nWhen a train crosses a platform, the total distance covered by the train is the sum of its own length and the length of the platform ($L_T + L_P$).
\nDistance = Speed $\\times$ Time.
\n$L_T + L_P = V_T \\times 20$.
\n$L_T + L_P = \\frac{50}{3} \\times 20 = \\frac{1000}{3}$ meters. (Equation 1)<\/p>\n
Case 2: Train crosses a person walking at 6 km\/hr in the same direction in 12 seconds.
\nThe speed of the person is 6 km\/hr. Convert this to m\/s.
\n$V_P = 6 \\times \\frac{5}{18} = \\frac{30}{18} = \\frac{5}{3}$ m\/s.
\nWhen the train crosses a person moving in the same direction, we use the relative speed.
\nRelative speed = Speed of train – Speed of person (since they are in the same direction).
\nRelative speed $= V_T – V_P = \\frac{50}{3} – \\frac{5}{3} = \\frac{45}{3} = 15$ m\/s.
\nThe distance covered by the train relative to the person is the length of the train ($L_T$).
\nDistance = Relative Speed $\\times$ Time.
\n$L_T = 15 \\times 12 = 180$ meters.<\/p>\n