A "Local" train leaves a station and runs at an average rate of 35 mph. An hour and a half later an "Express" train leaves the station and travels at an average rate of 56 mph on a parallel track. How many hours after it starts will the Express overtake the Local?
Step 1. Express distances (d1 and d2, d1 = d2 = d) using the formula for the speed v = d/t Step 2. Make the system of equations. Step 3. Solve the system of equations and express t2
Step 1. Local train parameters: rate: v1 = 35 mph time: t1 distance: d v1 = d/t1 d = v1 * t1 = 35*t1
Express train parameters: rate: v2 = 56 mph time: t2 = t1 - 1.5 h (because it is leaves hour and a half later then the local) distance: d v2 = d/t2 d = v2 * t2 = 56*(t1 - 1.5)
Step 2. Make the system of equations: d = 35*t d = 56*(t - 1.5)
Step 3. Solve the system of equations by using substitution method and calculate t2: 35t = 56(t1 - 1.5) 35t = 56t1 - 56*1.5 35t = 56t1 - 84 84 = 56t1 - 35t1 84 = 21t1 t1 = 84/21 t1 = 4
