it takes a passanger train 2 hous less time than it takes a

it takes a passanger train 2 hous less time than it takes a freight train to make the trip from central city to clear creek. the passenger train averages 96 km/h while the freight train averages 64 km/h. How far is it from central city to clear creek?

Solution

rate of passenger train = 96 kmh
rate of freight train = 64 kmh
time for freight train = t
time for passenger train = t-2
Using rate*time=distance
passenger train is:
96(t-2)=d
freight train is:
64(t)=d
Since both distances are the same, we set these two equations equal to one another:
96(t-2)=64t
clear the parentheses:
96t-192=64t
add (192 -64t) to both sides:
32t=192
divide by 32
t=6 hours
Let\'s find the distance using the same formulas:
64t=d
64(6)=d
384 km = distance
96(t-2)=d
96(6-2)=d
96(4)=d
384 km = distance
They are both the same so the distance is 384 km.