Train Question

Question

A train leaves New Orleans at 2:00 PM. A second train leaves the same city in the same direction at 4:00 PM. The second train travels 48mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains?

Answer 1

Let x = the rate of the first train

x + 48 = the rate of the second train

Time of the first train is 4 hours ( the second train left at 4:00 PM , that's 2 hours after the first train left at 2:00PM, then the second train overtook the first train at 6:00 PM, so the fist train has been traveling for 4 hours before the second train overtook it)

Time for the second train is 2 hours, from 4:00 PM to 6:00 PM

Distance = rate x time

Distance traveled by the first train = 4x

Distance traveled by the second train = 2 ( x + 48 )

4x = 2 ( x + 48 ) is the equation

4x = 2x + 96 using the distributive property

2x = 96 subtract 2x from both sides of the equation

x = 48 mph is the rate of the first train

x + 48 = 96 mph is the rate of the second train