A freight train leaves St. Louis traveling at 70 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 to find the time the first train spends traveling is h = d/70, where d is the distance traveled by the first train.
b) The second train leaves one hour later, so the first train has already traveled for h + 1 hours when the second train starts.
To find when the second train overtakes the first train, we need to solve the equation d = (h + 1) * 105, where d is the distance traveled by the second train.
Let's use the equation from part a to substitute for h in the equation above.
d = (d/70 + 1) * 105
d = (105d + 70) / 70 (simplified by multiplying both sides by 70)
Multiply both sides by 70 to get rid of the denominator.
70d = 105d + 70
-35d = 70
d = -2 (divided by -35 on both sides)
Since d represents distance, it cannot be negative, so the equation has no solution. This means that the second train will never overtake the first train.
c) Since the second train never overtakes the first train, the answer to part c cannot be determined.