# PhysicsTwo locomotives approach each other

#### karush

##### Well-known member
$\textsf{Two locomotives approach each other on parallel tracks.}\\$
$\textsf{Each has a speed of 155 km/h with respect to the ground.}\\$
$\textsf{If they are initially 8.5 km apart}\\$
$\textsf{a. how long will it be before they reach each other?}\\$
\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

#### skeeter

##### Well-known member
MHB Math Helper
closing speed is 310 km/hr

$t = \dfrac{d}{r} = \dfrac{8.5 \,km}{310 \,km/hr} \approx 1 \, min \, 39 \, sec$

#### HallsofIvy

##### Well-known member
MHB Math Helper
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.