Let the distance betwen the two cities,in miles = D
And....Distance / Rate = Time
And let's convert the rate to miles per minute.....60 mph = 1 mile per minute......45 mph = 3/4 miles per minute
So....equating the times, we have that 11 minutes added to the faster train's time = the slower train's time.......algebraically, we have :
D / 1 + 11 = D / (3/4) simplify
D + 11 = (4/3)D subtract D from both sides
11 = (1/3)D multiply both sides by 3
33 = D
Thus....the cities are 33 miles apart
Proof....the faster train covers this distance in 33 min.......the slower train takes (4/3) as long = (4/3)*33 = 4 * 11 = 44 minutes......so......the slower train takes 11 minutes longer