science physics
posted by julie on .
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?

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
Crossmultiply 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!