Speed of 2 trains.

Question

Two trains going in opposite directions leave at the same time. Train B travels 15 mph faster than train A. In 3 hours the trains are 345 miles apart. Find the speed of each.

Answer 1

Let's start with the fundamentals: Distance = Speed x Time 

                                        Units: miles =  miles per hour x hours 

 

I will define the variables as follows:

Speed of Train A = y 

Speed of Train B = y + 15 (since it states that "Train B travels 15 mph faster than train A")

Time = t = 3 (the time in hours) 

 

Approach to setting up the equation if that the distance traveled by Train B + distance traveled by Train A  = total distance 

 

[(y+15) × 3] + [(y) x 3] = 345     - First you can distribute the items in the brackets by multiplying each item by 3

3y + 45 + 3y = 345                     - Then you can combine both of the y terms 

6y + 45 = 345                             - Then subtract 45 from both sides of the equation 

     - 45     -45                             - Here I'm just showing the subtraction of 45 from each side 

6y = 300                                     - Finally you can divide both sides of the equation by 6 

  y = 50                                       - Now you have arrived at the speed of Train A (50 miles per hour!) 

 

Speed of Train A = y = 50 miles per hour 

Speed of Train B  = y + 15 = 65 miles per hour 

 

 

Let's double check this...Does distance traveled by Train B + distance traveled by Train A = total distance? 

 

Train A = (50 miles per hour) x (3 hours) = 150 miles traveled in a direction 

Train B = (65 miles per hour) x (3 hours) = 195 miles traveled in the opposite direction 

 

 

Yes! 150 miles + 195 miles = 345 miles total

 

 

 

Answer 2

Let's allow Train A to be x and Train B to be x+15. If we add these together we get 2x+15. We can now solve:

 

3 (2x+15)=345 (divide both sides by 3)

2x+15=115 (subtract both sides by 15)

2x=100 (divide both sides by 2)

x=50

 

So, Train A's speed is 50 mph and Train B's speed is 65 mph. Please let me know if that is helpful and if you would like to continue working through your questions together!

Answer 3

For train A, x_A=v*t

For train B, x_B=(v+15)*t

Where v is the speed for train A, X_A is the distance between the initial point and the position of train A at moment t and X_B is the distance between the initial point and the position of train B at moment t.

 

We know when t=3 hours, the distance between them is  345 mi, so x_A+x_B=345

 

x_A+x_B=v*t + (v+15)*t.

If we plug the vaules we know, we will have:

345= v*3 + (v+15)*3

(distributive property)

345= 3v + 3v +45

(substracting 45 both sides)

300=6v

(dividing both sides by 6)

50=v.

 

So, we know train A travels at 50mph and train B at 65mph (50+15).