Two trains leave the same train station at the same time, moving along straight tracks that form 35 angle. If one train travels at an average speed of 100 mi/hr and the other at an average speed of 90 mi/hr, how far apart are the trains after 30 min?

1 Answer
Nov 3, 2016

Answer:

Trains are #28.96# miles apart after #30# minutes.

Explanation:

The train with #100# mi/hr has moved in #30# min #100/(30/60)= 50#miles
The train with #90# mi/hr has moved in #30# min #90/(30/60)= 45#miles.
So this may be regarded as a triangle of which sides are #a=50 ; b=45# and their included angle is #/_C=35^0#

by applying cosine law, #c^2=a^2+b^2-2ab cosC or c^2= 50^2+45^2-2*50*45*cos35=2500+2025+4500*0.82=838.82(2dp)#
#c= sqrt 838.82=28.96# miles.

The trains are #28.96# miles apart after #30# minutes. [Ans]