Two trains a and b are 240 miles apart. both start at the same time and travel toward each other. they meet 3 hours later. the speed of train a is 20 miles faster than train b. find the speed of each train. (show work)

Train A = 50 mph; Train B = 30 mph

Step-by-step explanation:

In this case, let's call the speed of both trains as:

Va: speed of train A

Vb: speed of train B

As train A is faster than train B, let's call speed of train B as X; So if Vb is X, then Va would be:

Vb = X

Va = X + 20

If we combine both Speed, we have:

V = Va + Vb = X + X + 20 = 2X + 20

Now that we have an expression for the combined speed, let's recall the formula for speed in general:

V = d/t

Where:

d: distance = 240 miles

t: time = 3 hours

Combining all the data we have:

V = 240/3

but V is 2X + 20 so:

2X + 20 = 240/3

Solving for X:

2X + 20 = 80

2X = 80 - 20

2X = 60

X = 60/2

X = Vb = 30 mph

Now that we know speed of one train, we can know the speed of the other train:

Va = 30 + 20 = 50 mph

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