SOLUTION: This word problem has driven me crazy for a week. Please help me and show me how you came up with the answer.
Trains A and B are traveling in the same direction on parallel trac
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Trains A and B are traveling in the same direction on parallel trac
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Question 325143: This word problem has driven me crazy for a week. Please help me and show me how you came up with the answer.
Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 m.p.h. and Train B is traveling at 50 m.p.h.
Train A passes a station at 6:10 p.m.
If train B passes the same station at 6:40, at what time will Train B catch up to Train A ? Found 2 solutions by Theo, Alan3354:Answer by Theo(13342) (Show Source):
Trains A is traveling at 40 mph.
Train B is traveling at 50 mph.
Train A passes a station at 6:10 pm.
Train B passes the same station at 6:40 pm.
When will train B catch up with train A.
This is a rate * time = distance type of problem.
The rates will be given.
The distance will be the same for both trains.
The time will be different for both trains as shown below:
Since train A passes the station at 6:10 pm and train B passes the station at 6:40 pm, then train A will have traveled 1/2 hours more than train B.
If we let T = the time that train B travels, then the time that train A travels is T + .5
Formula for train A:
rate * time = distance
rate = 40
time = T + .5
distance = D
Formula for train A becomes:
40 * (T + .5) = D
Formula for train B:
rate * time = distance
rate = 50
time = T
distance = D
Formula for train B becomes:
50 * T = D
You need to solve these two equations simultaneously to get your answer.
The formulas are:
40 * (T + .5) = D
50 * T = D
Simplification of these two equations results in:
40*T + 40*.5 = D
50*T = D
Simplify further to get:
40*T + 20 = D
50*T = D
Subtract the first equation from the second equation to get:
10*T - 20 = 0
Add 20 to both sides of the equation to get:
10*T = 20
Divide both sides of the equation by 10 to get:
T = 2
You now know what T is.
If you substitute 2 for T in both equations you will get:
40*2.5 = D
50*2 = D
Solve for D to get:
40*2.5 = 100
50*2 = 100
D = 100 in both cases as it should.
The question is what time does train B catch up with train A.
Train B has passed the station at 6:40 pm.
Add 2 hours to that and you get 8:40 pm as the time that train B catches up with train A.
Train A has passed the station at 6:10 pm.
Add 2.5 hours to that and you get 8:40 pm as the time that train B catches up with train A.
You can put this solution on YOUR website! Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 m.p.h. and Train B is traveling at 50 m.p.h.
Train A passes a station at 6:10 p.m.
If train B passes the same station at 6:40, at what time will Train B catch up to Train A ?
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In 1/2 hour (640 - 610) train A goes 20 miles (1/2 x 40 mph)
Train B gains on train A at 10 mph (50 - 40)
It takes train B 2 hours to overtake train A (20/10)
6:40 + 2 hours = 8:40
