Problema Solution
A train leaves Perryville at 6:00 A.M. and travels east at a rate of 64 mph. As it reaches its destination, Granite City, a westbound train departs from Granite City to Perryville, traveling at a rate of 48 mph. How far is it from Perryville to Granite City by train if the westbound train gets to Perryville at 9:30 A.M.?
Answer provided by our tutors
let
v1 = 64 mph the rate of the train traveling from Perryville to Granite City
t1 = the time of the travel from Perryville to Granite City
v2 = 48 mph the rate of the train traveling from Granite City to Perryville
t2 = the time of the travel from Granite City to Perryville
the total time of the travel back and forth is 9:30 AM - 6:00 AM = 3.5 hours thus
t1 + t2 = 3.5
since ditance = speed*time we have:
v1t1 = v2t2
64t1 = 48t2 divide both sides by 16
4t1 = 3t2
by solving the system of equations:
t1 + t2 = 3.5
4t1 = 3t2
we find:
t1 = 1.5 hr
t2 = 2 hr
click here to see the step by step solution of the system of equations:
distance = v1*t1 = 64*1.5 = 96 miles
there is 96 miles distance between Perryville and Granite City.