MHB *Two locomotives approach each other

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Two locomotives traveling towards each other at 155 km/h are initially 8.5 km apart. The closing speed of the locomotives is 310 km/h, leading to a calculated time of approximately 1 minute and 39 seconds for them to meet. This is derived from the formula t = d/r, where d is the distance and r is the relative speed. Both methods of calculation confirm that the time to collision is about 99 seconds. The discussion emphasizes the importance of understanding relative speed in such scenarios.
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$\textsf{Two locomotives approach each other on parallel tracks.}\\$
$\textsf{Each has a speed of 155 km/h with respect to the ground.}\\ $
$\textsf{If they are initially 8.5 km apart}\\$
$\textsf{a. how long will it be before they reach each other?}\\$
\begin{align*}\displaystyle
t&=\frac{d}{r}\\
&=\frac{1}{2}\cdot\frac{8.5}{155}\\
&\approx0.0274 \, h \\
&\approx\color{red}{99 \, seconds}
\end{align*}

ok this looks very simple
so I'm sure I got it wrong
 
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closing speed is 310 km/hr

$t = \dfrac{d}{r} = \dfrac{8.5 \,km}{310 \,km/hr} \approx 1 \, min \, 39 \, sec$
 
Either argue, as skeeter does, that relative to one of the locomotives, the other has speed 155+ 155= 310 kph and has to go distance 8.5 km so will take time $\frac{8.5}{310}= 0.0274$ hours so 0.0274(60)= 1.6451 min= 1 min 39 seconds.

Or argue, as you apparently do, that, since the two trains have the same speed, 155 kph, and must cover half the distance, 8.5/2= 4.25 km, the time will be $\frac{4.25}{155}= 0.0274$ hours so 0.0274(60)= 1.6451 min= 1 min 39 seconds.

1 min 39 seconds is, of course, 60+ 39= 99 seconds as you say.
 
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