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 that would be used to find the time the first train spends traveling can be written as: h = t + 1, where h is the time the first train spends traveling and t is the time it takes for the second train to overtake the first train.
b) To find the time it takes for the second train to overtake the first train, we can set up a proportion using the distance covered by both trains. Since the second train overtakes the first train, their distances traveled will be the same.
The formula for distance is distance = speed x time.
Distance covered by the first train = speed of the first train x time of the first train = 80h
Distance covered by the second train = speed of the second train x time of the second train = 105t
Setting up the proportion: 80h = 105t
We can solve this equation for t:
t = (80h) / 105
Given that h = t + 1, we can substitute this value into the equation above:
t = (80(t+1)) / 105
To find the value of t, we can solve this equation:
105t = 80t + 80
25t = 80
t = 80/25
t ≈ 3.2
Therefore, the second train overtakes the first train approximately 3.2 hours after the first train left.
c) To find the distance traveled when the second train catches up, we can substitute the value of t into the equation for the distance covered by the second train:
Distance = 105t = 105 x 3.2 = 336 kilometers
Therefore, when the second train catches up, both trains have traveled approximately 336 kilometers.