Problema Solution
A train leaves a station traveling at the rate of 40 miles per hour. 2 hours later a second train leaves the same station traveling in the exact opposite direction at a rate of 60 miles per hour. How long after the second train left the station will the two trains be 430 miles apart?
Answer provided by our tutors
let
v1 = 40 mph the rate of the first train
t1 = the time of travel of the first train
v2 = 60 mph the rate of the second train
t2 = the time of travel of the second train
d = 430 miles the distance between them
t1 = t2 + 2
since speed = distance/time => distance = speed*time
v1*t1 + v2*t2 = d
40t1 + 60t2 = 430 divide both sides by 10
4t1 + 6t2 = 43
by solving the system of equations
t1 = t2 + 2
4t1 + 6t2 = 43
we find
t2 = 3.5 hr
click here to see the step by step solution of the system of equations
3.5 hours after the second train leaves the station the two trains will be 430 miles apart.