Thomas the tank Engine leaves the station at 3 p.m. traveling at a speed of 70 mph. Percy leaves the station at 5 p.m. traveling at 110 mph. Write 2 parametric pairs to model the trains motion. If they are traveling on parallel tracks at what time will Percy be at the same point as Thomas? How far away from the station are they when that happens? thanks

Question

anonymous · Answer

r*t = d
Let t be the elapsed time in hours that Percy takes to catch up to Thomas.
At this elpased time, both have traveled the same distance from the station.
Solve the following equation for t:
70*2+70t = 110t
t = 7/2 hours  The intercept time of day is 5 pm + 3.5 hours or 8:30 pm .
The intercept point is 3.5 hrs * 110 miles/hr or 385 miles from the station.