A freight train leaves St. Louis traveling at 70km/hr.
One hour later, a passenger train leaves St. Louis on a parallel track traveling 105 km/hr.
When will the 2nd train overtake the first train?
How far from St. Louis will the passenger train overtake the freight train?
a) Let h= the time the first train spends traveling. Write the equation you would use to find this time.
b) hours after the first train left, the 2nd train overtakes the first train. (Round to one decimal place.)
c) When the 2nd train catches up, the trains have traveled kilometers.
a) The equation to find the time spent traveling by the first train can be written as:
Distance = Speed * Time
Let d = distance traveled by the first train
Let t = time spent traveling by the first train
Therefore, the equation becomes:
d = 70t
b) Since the second train leaves one hour later than the first train, the equation to find when the second train overtakes the first train can be written as:
Distance2ndTrain = Distance1stTrain + Speed2ndTrain * (Time2ndTrain - Time1stTrain)
d = 70t + 105(t - 1)
105(t - 1) = 70t
105t - 105 = 70t
35t = 105
t = 3 hours (rounded to one decimal place)
c) To find the distance traveled by the trains when the second train catches up, substitute the value of t into the equation for Distance2ndTrain:
Distance2ndTrain = 70t + 105(t - 1)
= 70 * 3 + 105(3 - 1)
= 210 + 105(2)
= 210 + 210
= 420 kilometers