Lesson A train passing a telegraph post and passing a bridge
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<H2>A train passing a telegraph post and passing a bridge</H2> <H3>Problem 1</H3>A train takes 4 seconds to pass a telegraph post and 20 seconds to pass a 256 m long bridge. Find the length of the train and its speed. <B>Solution</B> Let <B>L</B> be the train's length (in meters) and let <B>u</B> be the train's speed (in meters per second). Since the train takes 4 seconds to pass a telegraph post, it gives an equation {{{L/u}}} = {{{4}}}. Since the train passes a 256 m long bridge in 20 seconds, it gives you another equation {{{(256 + L)/u}}} = {{{20}}} (the train should move the distance equal to the bridge's length plus its own length - it means "the train passes the bridge"). Thus you need to solve the system of two equations in two unknowns {{{system (L/u = 4, (256 + L)/u = 20)}}}. Express <B>L</B> from the first equation {{{L}}} = {{{4u}}} and then substitute it into the second equation. You will get {{{(256 + 4u)/u}}} = {{{20}}}. Simplify it step by step: 256 + 4u = 20u, 256 = 20u - 4u, 256 = 16u, {{{u}}} = {{{256/16}}} = {{{16}}}. Thus the train's speed is 16 {{{m/s}}} = 57.6 {{{km/h}}}. It implies that the train's length is {{{L}}} = {{{4u}}} = {{{4*16}}} = {{{64}}} {{{m}}}. <B>Answer</B>. The train's length is 64 m. The train's speed is 16 {{{m/s}}}. 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