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( PLEASE HELP ) Train A leaves a train station at noon, traveling at a constant speed of 80 miles per hour. Train B leaves the same station on a parallel track at PM, traveling a constant speed, and catches up with Train A at 5 PM. How fast, in miles per houris Train B going?

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Answer:

266.67 miles per hour.

Explanation:

Let's call the speed of Train B "x" (in miles per hour). We can start by using the formula:

distance = rate x time

Let's call the distance that Train A travels before Train B catches up "d". We know that Train A travels for 5 hours at a speed of 80 miles per hour, so its distance traveled is:

d = 80 x 5 = 400 miles

Now let's consider Train B. We know that it travels for 5 - p hours (where "p" is the number of hours it takes Train B to catch up with Train A) at a speed of "x" miles per hour. Its distance traveled is:

d = x(5 - p)

Since Train B catches up with Train A when they have both traveled the same distance, we can set these two expressions for "d" equal to each other:

80 x 5 = x(5 - p)

Simplifying this expression:

400 = 5x - xp

We don't know the value of "p", but we can use another piece of information from the problem to solve for it. We know that Train B leaves the station at some time "p.m." after noon. This means that it travels for "12 + p" hours, since there are 12 hours between noon and midnight. So we can write:

5 - p = 12 + p

Simplifying this expression:

p = 3.5

Now we can substitute this value of "p" into our equation for "x":

400 = 5x - (3.5)x

Simplifying this expression:

400 = 1.5x

Dividing both sides by 1.5:

x = 266.67

Therefore, Train B is traveling at a speed of approximately 266.67 miles per hour.

User Adenike
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