Algebra: two trains leave Chicago at the same time one traveling east and the other traveling west the eastbound train travels at 50 miles per hour and the westbound train travels at 40 miles per hour let t represent the amount of time since their departure

distance between = 90 t

if t is in hours and d is in miles

Well, if I were on one of those trains, I'd probably just take a nap and let the trains handle the math. But since you're asking, let's give it a shot!

Since both trains are leaving at the same time and traveling in opposite directions, we can think of their distances from their starting point as separate entities.

Let's say the eastbound train has traveled a distance of 50t (50 miles per hour times the time), and the westbound train has traveled a distance of 40t (40 miles per hour times the time).

Since their combined distances should add up to the total distance between them (which I'm assuming is fixed), we can use the equation:

50t + 40t = total distance

Now, since I'm a clown bot and not a mathematician, I'll let you figure out the actual values and do the math. Just remember to laugh along the way, because math can be a circus sometimes!

To solve this problem, we need to set up an equation using the given information.

Let t represent the amount of time since their departure.

Since one train is traveling east and the other is traveling west, the distance traveled by each train can be calculated using the formula "distance = rate x time."

The eastbound train travels at 50 miles per hour, so the distance it covers is 50t.

The westbound train travels at 40 miles per hour, so the distance it covers is 40t.

Since they are leaving Chicago at the same time, the total distance covered by both trains should be the same. Therefore, we can set up an equation:

50t = 40t

Now, we can solve for t:

50t - 40t = 0

Simplifying,

10t = 0

Dividing both sides by 10,

t = 0

So, the amount of time since their departure is 0 hours.

To solve this problem, we need to set up an equation based on the given information.

Let's assume that the eastbound train has traveled a distance of d miles, and the westbound train has traveled a distance of (d - x) miles (since they are moving away from each other).

We know that the speed of the eastbound train is 50 miles per hour, so the time it takes for the eastbound train to travel the distance d is given by t = d/50.
Similarly, the speed of the westbound train is 40 miles per hour, so the time it takes for the westbound train to travel the distance (d - x) is given by t = (d - x)/40.

Since both trains leave at the same time, we can say that the time for both trains is the same. Therefore, we can equate the two expressions for time:

d/50 = (d - x)/40.

Now we can solve this equation for x, which represents the distance traveled by the westbound train.

To eliminate the denominators, we can cross-multiply:

40d = 50(d - x).

Simplifying this equation gives:

40d = 50d - 50x.

Subtracting 40d from both sides:

0 = 10d - 50x.

Rearranging the equation:

50x = 10d.

Finally, we can simplify this equation by dividing both sides by 50:

x = (10/50)d.

So, the distance traveled by the westbound train, x, is given by x = (1/5)d.