A freight train leaves St. Louis traveling at 80 km/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 we would use to find the time spent traveling by the first train is:
Distance = Speed × Time
Since the first train travels at a speed of 80 km/hr and it travels for time h, the equation becomes:
Distance = 80h
b) To find the time after the first train left when the second train overtakes it, we need to set up the equation:
Distance of first train = Distance of second train
80h = 105(t-1)
Where t is the time in hours for the second train to overtake the first train. We subtract 1 from t because the second train leaves one hour later.
Simplifying the equation:
80h = 105t - 105
105t - 80h = 105
t = (105 + 80h) / 105
Now we can substitute the value of h into the equation to find t.
c) When the second train catches up, the distance traveled by both trains will be the same. Using the equation Distance = Speed × Time, we can calculate the distance traveled by each train.
Distance of first train = 80h (from part a)
Distance of second train = 105t
Since the distances are the same, we can set up the equation:
80h = 105t
Now we can substitute the value of t found in part b to calculate the distance:
Distance = 80h = 105[(105 + 80h) / 105]