solving a distance, rate, and time problem using linear equations

Question

 two trains leave stations 364 miles apart at the same time and travel towards each other. one travels at 55mph while the other travels at 75 mph. how long will it take the two trains to meet? 

 

Answer 1

Sam,

 

Let   t = travel time, identical for both trains since they leave simultaneously.

     d₁ = distance traveled by the 55 mph train  = 55t  (distance = speed multiplied by time)

     d₂ = distance traveled by the 75 mph train  = 75t

 

Since they are traveling towards each other, the total distance they must travel in time t to meet is the distance between the train stations, 364 miles.

 

Thus  d₁ + d₂ = 364

        55t + 75t = 364,   so 130t = 364  and   t = 364/130 = 2.8 hours

 

And they will meet at d₁ = 55(2.8) = 154 miles from the slower train's station, or 210 miles from the other station.

Answer 2

Hey Sam,

 

364 miles = (55 mph + 75mph) (t)

 

364 miles = (130 mph) (t)

 

t = 2.8 hrs = 2 hrs 48 minutes.

 

2.8 x 55 + 2.8 x 75 = 154 + 210 = 364

 

From this conclusion, the train (1) with 55 mph needs to travel 154 miles (for 2.8 hrs) and the train (2) with 75 mph needs to travel 210 miles (for 2.8 hrs) to meet each other.

 

It will take 2.8 hrs or 2 hrs 48 minutes for 2 trains to meet each other.

 

Note: 0.8 hr = 80% of 1 hr = 80% of 60 minutes = 48 minutes.

 

I hope you got this.  Good luck.