A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

$$\eqalign{ & {\text{Speed}} = \left( {78 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\frac{{65}}{3}} \,{\text{m/sec}} \cr & {\text{Time = }}\,{\text{1}}\,{\text{minute = 60}}\,{\text{second}}. \cr & {\text{Let}}\,{\text{the}}\,{\text{length}}\,{\text{of}}\,{\text{the}}\,{\text{tunnel}}\,{\text{be}}\,x\,{\text{metres}}. \cr & {\text{Then}},\, {\frac{{800 + x}}{{60}}} = \frac{{65}}{3} \cr & \Rightarrow 3\left( {800 + x} \right) = 3900 \cr & \Rightarrow x = 500 \cr} $$