Question #16fdc
1 Answer
After 12 hours (720 min) train 2 would catch up with train 1.
Explanation:
If we call the station (0,0) on a coordinate plane then we can use it to relate the two speeds. We know that train one (t1) is traveling at a constant speed (no acceleration) for three hours before train two (t2) gets going.
By multiplying the time that has lapsed by the the speed we can find the the distance traveled in the given time:
80mi/h⋅30h
= 240mi
Now that we have the displacement traveled after 3 hours we can use this distance to relate the two speeds with a standard kinematic equation:
However because a=0 everything to the right of the (+) is turned to zero and becomes irrelevant. This leaves us with:
After imputing each velocity in the equation we are left with
t1
and
t2
But before we can combine the equations and solve for t, we need to relate the displacements. Currently t1's displacement is relative to 240 mi from the station, while t2's displacement is relative to the train station. To fix this, we must add 240 mi to t2's
displacement to allow us to find the time when t2 has caught up to t1. After adding the 240 mi to t2's displacement we get:
t1
and
t2
Now that t1 and t2 are on the same page we can combine the equations and sovle for t:
We can double check our answer by multiplying each speed by our time and adding 240 miles to t1:
t1
(We add 240mi to account for the 3h head start that t1 got)
t2
