Question 983846


Let &nbsp;<B>L</B>&nbsp; be the train's length &nbsp;(in meters)&nbsp; and let &nbsp;<B>u</B>&nbsp; be the train's speed &nbsp;(in meters per second).


Since the train takes &nbsp;4&nbsp; seconds to pass a telegraph post, &nbsp;it gives an equation 


{{{L/u}}} = {{{4}}}.


Since the train passes a &nbsp;264 m long bridge in &nbsp;20 seconds, &nbsp;it gives you another equation 


{{{(264 + L)/u}}} = {{{20}}}


(the train should move the distance equal to the bridge length plus its own length - it means &nbsp;"to pass the bridge"). 


Thus you need to solve the system of two equations in two unknowns


{{{system (L/u = 4,
(264 + L)/u = 20)}}}.


Express &nbsp;<B>L</B>&nbsp; from the first equation &nbsp;{{{L}}} = {{{4u}}}&nbsp; and then substitute it into the second equation. &nbsp;You will get 


{{{(264 + 4u)/u}}} = {{{20}}}.


Simplify it step by step:


264 + 4u = 20u,


264 = 20u - 4u,


264 = 16u,


{{{u}}} = {{{264/16}}} = {{{16.5}}}.


Thus the train's speed is &nbsp;16.5 {{{m/s}}}. 


It implies that the train's length is &nbsp;{{{L}}} = {{{4u}}} = {{{4*16.5}}} = {{{66}}} {{{m}}}.


<B>Answer</B>. &nbsp;The train's length is &nbsp;66 m. &nbsp;The train's speed is &nbsp;16.5 {{{m/s}}}.