A freight train leaves St. Louis traveling at 85 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 by the first train traveling is h=x/v, where x represents the distance traveled by the first train and v represents its velocity.
b) To find the time when the second train overtakes the first train, we can use the equation t = h + 1, where t represents the time the second train spends traveling (since it departs one hour later) and h represents the time spent by the first train traveling. Let's substitute the values in the equation to find t: t = (x/v) + 1.
c) When the second train catches up, the trains have traveled the same distance. Let's call this distance y. The distance traveled by the first train is x = v_h, where v_h represents the velocity of the first train and h represents the time it spends traveling. We know that the velocity of the first train is 85 km/hr, so x = 85h. The distance traveled by the second train is y = v(t+1), where v represents the velocity of the second train and t represents the time it spends traveling. We know that the velocity of the second train is 105 km/hr, so y = 105(t+1). When the second train catches up, x = y, so 85h = 105(t+1).