BTGModeratorVI wrote: ↑Wed Apr 22, 2020 11:07 am
Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?
a) 70
b) 85
c) 95
d) 105
e) 120
Answer:
E
Source: Veritas Prep
Solution:
We are given that trains A and B are traveling toward each other, so we have a “converging rate problem,” in which we can use the formula:
Distance traveled by train A + Distance traveled by train B = total distance
Since the two trains started 190 miles apart, the total distance is 190, so we have:
Distance traveled by train A + Distance traveled by train B = 190
We are given that train A travels at a rate of 15 mph and leaves one hour before train B. We are also given that train B travels at a rate of 10 mph.
We can let the time of train B = t and, since train A left one hour earlier and thus will have traveled for one more hour than train B, at the time they meet, the time of train A = t + 1.
Since rate x time = distance, we can calculate the distance, in terms of t, of both trains A and B.
Distance of train A = 15(t + 1) = 15t + 15
Distance of train B = 10t
Now we can substitute these values into our total distance formula and determine t.
15t + 15 + 10t = 190
25t = 175
t = 7
Thus, when the trains meet, train A has traveled (15 x 7) + 15 = 120 miles.
Alternate Solution:
After one hour, train A has traveled 15 miles, so the distance between the two trains is 190 - 15 = 175 miles.
When both trains are moving, the distance between them is decreasing 15 + 10 = 25 miles each hour; therefore, the two trains will meet in 175/25 = 7 hours. Together with the first hour, train A has traveled 1 + 7 = 8 hours in total, and thus when the two trains met, train A has traveled 8 * 15 = 120 miles.
Answer: E
