Problema Solution
A slow train leaves town X at 9:25am and arrives at town Y at 12:20pm. On the same day the Tangara Express leaves town X at 10:04am to arrive at Y at 11:44am. Obviously, along the way, the Tangara Express train has passed the slow train, but, if both trains are travelling at constant speeds, at what time do the trains pass each other?
Answer provided by our tutors
let
v1 = the speed of the slow train
v2 = the speed of the Tangara Express train
the time of the travel of the slow train is 12:20 pm - 9:25 am = 2h 55 min = 2 + 55/60 = 2 + 11/12 = 35/12 hr
the time of the travel of Tangara Express is 11:44 am - 10:04 am = 1h 40 min = 1 + 40/60 = 1 + 2/3 = 5/3 hr
since they both pass same distance and we know that distance=speed*time we have the following equation
(35/12)v1 = (5/3)v2 multiply both sides by (3/5)
v2 = (3/5)(35/12)v1
let t = the time of the travel of the Tangara Express train until the moment they pass each other
since slow trains starts 10:04 am - 9:25 am = 39 min earlier its time until the pass is: t + 39/60
v1(t + 39/60) = t*v2
plug v2 = (3/5)(35/12)v1 into the last equation
v1(t + 39/60) = t*(3/5)(35/12)v1 divide both sides by v1
(t + 39/60) = t*(3/5)(35/12)
by solving for t we find
t = 13/15 hr
t = 13*60/15
t = 52 min
click here to see the step by step solution of the equation
52 min after 10:04 am is 10:57 am.
the trains will pass each other at 10:57 am.