How do I set up uniform motion problems?

Question

Two trains are traveling towards each other. One is traveling at twice the speed of the other. They started traveling at the same time from two separate stations that are 306 miles apart. In three hours the trains pass each other. Find the rate that each train is traveling.

The slower train is traveling at ____ mph

The faster train is traveling at ____ mph

Answer 1

Remember that since the trains are heading towards each other, their speeds add up. Think of it like this, if Train A is going 100 MPH. and Train B is going 200 MPH, it is the same math as if Train A was going 0 MPH (not moving) and Train B was going 300 MPH.

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First, write out your givens and equations that will be used :

T = 3 hours (This is given in "'In three hours the trains pass each other")

V_A = 2*V_B (This is given in "One is traveling at twice the speed of the other")

V_T = V_A + V_B = 2V_B + V_B = 3V_B (As stated before, relative Velocity is the sum of the 2 trains' velocities)

D = 306 Miles (They started traveling at the same time from two separate stations that are 306 miles apart.)

D = T*V_T (This is the standard distance covered formula... Time * Velocity)

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Solve V_B : plug your known variables of T & D into the equation for D

D = T*V_T

306 = 3*V_T

Divide both sides by 3

102 = V_T

Substitute 3V_B for V_T (remember, this was a given up above)

102 = 3V_B

Divide both sides by 3

34 = V_B (SLOWER train)

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Solve V_A

V_A = 2*V_B

V_A = 2*34

V_A = 68 (FASTER train)

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Always check your work!!

V_A = 68

V_B = 34

D_A = 68 miles/hour* 3 hours = 204 miles

D_B = 34 miles/hour* 3 hours = 102 miles

204 + 102 = 306, which is the total miles traveled.

Answers are CORRECT!