Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 236 miles in the same time that Dana travels 224 miles. If Chuck’s rate of travel is 3 mph more than Dana’s, and they travel the same length of time, at what speed does Chuck travel?

r mi/h = Dana's rate.

r * t = 224 miles.
t = 224/r.

3)224r+3) mi/h = Chuck's rate.
(r+3)t = 236
Replace t with 224/r:
(r+3)224/r = 236
Multiply both sides by r:
(r+3)224 = 236r
224r + 672 = 236r
236r - 224r = 672
12r = 672
r = 56 mi/h = Dana's speed.
r+3 = 59 mi/h = Chuck's speed.

Correction: Chuck's rate = (r+3)mi/h.

To find the speed at which Chuck travels, we need to set up an equation based on the given information. Let's call Chuck's speed "x" mph and Dana's speed "y" mph.

We know that Chuck travels 236 miles and Dana travels 224 miles. We also know that they both travel for the same amount of time.

Using the formula speed = distance / time, we can write the following equations:

Chuck's speed: x = 236 / t
Dana's speed: y = 224 / t

Note that we don't know the exact time it took for them to travel, so we represent it as "t" here.

It is also given that Chuck's speed is 3 mph more than Dana's speed, so we can write another equation:

x = y + 3

Now we can solve these equations simultaneously to find the value of x.

Rearranging the first equation, we get t = 236 / x.
Rearranging the second equation, we get t = 224 / y.

Since they both represent the same time, we can set them equal to each other:

236 / x = 224 / y

Next, substitute x = y + 3 into this equation:

236 / (y + 3) = 224 / y

Now, cross-multiply and solve for y:

236 * y = 224 * (y + 3)
236y = 224y + 672
12y = 672
y = 672 / 12
y = 56

Thus, Dana's speed is 56 mph.

Finally, substitute this value back into the equation x = y + 3 to find Chuck's speed:

x = 56 + 3
x = 59

Therefore, Chuck travels at a speed of 59 mph.