Word problem about trains leaving a station at different mph

Question

At 3:25pm, two trains left Los Angeles.  One train traveled westward at a constant rate of 82 mph, while the other train traveled east at a constant rate of 66 mph.  If they are now 111 miles apart, what time is it now?

 

Solve using a system of equations.

 

Please show all steps

Answer 1

Hi Brooke, to tell you the truth, I do not think I would want to be on a train leaving the Los Angeles station at 3:25 PM heading west at 82 miles per hour. I do not swim very well!!!

 

The answer to the question is 4:10 PM. Here is the way to get to the answer.

 

Use the D(istance) = R(ate) * T(ime) formula. We know the distance the trains are apart is 111 miles. The rates of the two trains are given. The time is the same for both trains.

 

Here is the equation:

 

R_w * T + R_e * T = D, where R_w is the rate of the train heading west, R_e is the rate of the train heading east, T is the time of travel for the trains, and D is the distance they are apart.

 

Substitute and find the value of T:

 

82 * T + 66 * T = 111

 

148T = 111

 

Divide both sides by 148:

 

T = .75, or the trains have traveled for .75 hours, which is 45 minutes.

 

3:25 PM + 45 minutes is: 4:10 PM.

 

Questions?

Answer 2

d = rt

Let t₁ = time that the westward train traveled

let t₂ = time the eastward train traveled

t₁ + t₂ = total time = t

 

d₁ = 82t₁  and d₂ = 66t₂

 

Total distance = d₁ + d₂ = 111

82t₁ + 66t₂ = 111

148t = 111

t = .75 hours

3/4 of an hour is 45 minutes. So, the time is now 4:10 p.m.