Question

Two locomotives approach each other on parallel tracks. Each has a speed of v = 95 km/h with respect to the ground. If they are initially d = 7.5 km apart, how long will it be before they reach each other?

Answer 1

The speed at which the two objects are approaching each other (from the trains' perspective) is 95 km/h (x 2) = 190 km/h.

If they are 7.5 km apart at first, you can set up a proportion:

190 km 7.5 km
------ = ---------
1 hr x hr


Cross-multiply the terms and set them equal to each other.

(190 km)(x hr) = (7.5 km)(1 hr)


Divide both sides by (190 km).

(190 km)(x hr) = (7.5 km)(1 hr)
-------------- --------------
190 km 190 km


x hr = (7.5 kmh)/190 km

x hr = 0.03947368421 hr.
(sig figs = 0.039 hr)



The unit of hr. may not be very useful in this case, so let's convert hrs to min using dimensional analysis:

0.03947368 hr 60 min
------------- x ------------

1 1 hr


= 2.36 minutes
(sig figs = 2.4 minutes)

Hope this helps!