Krystal: Algebra fun with train A and train B?
Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and B at 70 mph. Train A passes a train station at 8:15 PM. If train B passes the same station at 8:27 PM at what time will train B catch up to train A?
Answers and Views:
Answer by what is math
We know that at t_0 := { d_a and d_b = 0}. Passing the train station after 12 minutes means that d_a = v_a*(12/60) = (60)(12/60) = 12 miles. So train A is ahead by 12 miles. This means that its function is : x(t) = x_o + v_o*t = 12 + 60t. A function describing the distance of train B at any time t is x(t) = v_b*t = 70t
12 + 60t = 70t
12 = 10t
t = 12/10 = 1.2 hours or 72 minutes for train B to catch up
d1= r1 x t1
d2 = r2 x t2
d1 = d2
r1 x t1 = r2 x t2
70 x (t -12) = 60 x (t)
70t – 840 = 60t
10t = 840
t = 84 minutes
check
since the 60 mi/hr train goes one mile per minute, it is 12 minutes and 12 miles ahead when train B passes the station
70 mi/60 min x 72 min = 84 miles
60 mi/60 min x 72 min = 72 miles
8:15 plus 84 minutes = 9:39 PM
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