chuck and dana agree to meet in florida for the weekend. Chuck travel 152 miles in the same time that Dana travels 132 miles. If chuck rate of travel is 5 mph more than Dana and they travel the same length of time, at what speed does chuck travel

Dana's speed = r mi/h

Chuck's speed = (r+5) mi/h

r*t = 132 mi.
t = 132/r = Dana's time.

(r+%)*t = 152
t = 152/(r+5) = Chuck's time.
Dana's time = Chuck's time:
132/r = 152/(r+5).
Solve for r.

To determine Chuck's speed of travel, we can solve this problem using the concept of relative speed.

Let's assume Dana's speed as 'x' mph. Since Chuck's speed is 5 mph more than Dana, his speed can be represented as 'x + 5' mph.

We know that Chuck traveled 152 miles in the same time that Dana traveled 132 miles.

To find the time taken, we can use the formula: Time = Distance / Speed.

For Chuck's journey, we have: Time taken by Chuck = Distance traveled by Chuck / Chuck's speed = 152 / (x + 5) hours.

For Dana's journey, we have: Time taken by Dana = Distance traveled by Dana / Dana's speed = 132 / x hours.

Since both Chuck and Dana traveled the same length of time, we can set the two equations equal to each other:

152 / (x + 5) = 132 / x.

We can now solve this equation to find the value of 'x', which represents Dana's speed.

To simplify the equation, we can cross-multiply:

152x = 132(x + 5).

152x = 132x + 660.

Now, let's subtract 132x from both sides:

20x = 660.

Divide both sides by 20:

x = 33.

Therefore, Dana's speed is 33 mph.

To find Chuck's speed, we can substitute this value back into the equation:

Chuck's speed = Dana's speed + 5 = 33 + 5 = 38 mph.

So Chuck travels at a speed of 38 mph.