Train speed and time question.

Question

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and train B is traveling at 70 mph. Train A passes a station at 12:20 P.M. If train B passes the same station at 12:32 P.M, at what time will train B catch up to train A?

Answer 1

Hi Kari, the best way to solve this type of problem is to create a table with the given information using the distance equal to rate times time equation, D(istance) = R(ate) * T(ime)

 

Train      Distance       Rate       Time

---------------------------------------------

A                              60mph     x + .2    <== The .2 represents the difference in time between Train A and Train B reaching the same station converted to hours (12 min = .2 hours)

 

B                              70mph     x

 

In order for train B to catch train A, the distance for both must be the same. Because the distance must be the same, we can set the distance train A travels equal to the distance train B travels until they meet.

 

D_A = 60 * (x + .2)

 

D_B = 70 * x

 

D_A = D_B

 

Substitute for D_A and D_B

 

60 * (x + .2) = 70x

 

Clear parentheses:

 

60x + 12 = 70x

 

Subtract 60x from both sides:

 

10x = 12

 

Divide both sides by 10:

 

x = 1.2

 

Train B will catch train A in 1.2 hours or 1 hour and 12 minutes.

 

The time train B catches train A will be 12:32 PM plus 1 hour and 12 minutes or 1:44 PM.

 

Questions?