I have a question about a College Algebra word problem.

Question

two trains are at stations which are 800 miles apart. if they start traveling toward each other at the same time, one averaging 67 mph and the other averaging 53 mph, in how many hours will they pass each other? with steps please.

Answer 1

Since the trains leave the station at the same time and pass each other at the same time, the total time traveled at the point that they pass each other is the same. If we define t at the time in hour that the two trains pass each other, then the distance traveled by the first train is 67 mph + t hours and the distance traveled by the second train is 53 mph + t hours. We also know that the distanced traveled by both trains combined is 800 miles we can create the equation 67t + 53t = 800. We can then solve this for t and we get 6.67 hours as the answer.

Answer 2

1st we need to setup our two equations one for each train to find the distance each of them will travel

 

train 1 traveling at a speed of 67miles per hour will travel for X hrs will cover distance = 67X miles

train 2 traveling at a speed of 53miles per hour will travel the same time of X hrs to cover a distance of 53X miles

 

together they will cover total 800 miles

 

so lets put all of the pieces together to from an equation we can solve.

 

67X+53X = 800 miles

 

combine like terms

120X =800

 

divide both sides by 120

120X/120 =800/120

 

X = 6.67 hrs

each train will have traveled for 6.67 hrs when they pass each other.