Two trains speed

Question

Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 5 hours the trains are 525 miles apart. Find the speed of each train? 

Answer 1

Hi Ryan,

 

Let Train A rate = A

Let Train B rate = B

 

B = A + 5

 

A train travels X miles

B train travels 525 - x miles

 

Time for each train is the same = 5

 

Time = Distance/Rate

 

(525-X)/(A + 5) = 5

 

X/A = 5 --> 5A = X

 

Substitute 5A for X in the first equation:

 

(525 - 5A) / (A + 5) = 5

 

Cross multiply:

 

5A + 25 = 525 - 5A

 

10A = 500

 

A = 50 mph = train A speed

 

B = 55 mph =  train B speed

 

Check the answer by figuring out how far each train goes in 5 hours and add up the distances to see if it equals 525 miles.

 

 

Answer 2

So you know that the trains are moving in opposite direction and so the distance between the two trains will be the sum of the distances each train traveled.

Let's set the speed of train A = x.

Now you know that the speed of train B is 5mph faster than that of A of set the speed of train B = x+5.

They both traveled 5 hours and are 525 miles apart, meaning that the sum of the distances each train traveled is 525 mi.

The formula that relates distance, speed, and time is:

Distance = speed * time

 

Knowing this, let us calculate the distances each train traveled and add them together to get 525 miles.

Train A: distance train A traveled = 5 hours * x = 5x

Train B: distance train B traveled = 5 hours * (x+5) = 5x+25

 

Then you know that the sum of the two distances is 525 so:

5x + 5x+25 = 525

 

Add the x values and move the numerical values to the right hand side of the equation (subtract 25 from both sides of the equation) to get:

10x = 500

 

Divide by 10 on both sides of the equation to get:

x=50 mph

 

So if x = 50 mph and x is the speed of train A, then the speed of train B is 5+50 = 55 mph

 

Speed of train A = 50 mph

Speed of train B = 55 mph

 

Note: You can check your answer by plugging those numbers into an equation of the sum of the distances:

distance of train A + distance of train B = 50 mph (5 hours) + 55 mph (5 hours) = 250 mi + 275mi = 525mi.

You got 525 mi. which is the number that was given in the problem!