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?
To solve this problem, we can use the formula:
Distance = Rate x Time
Let's denote Dana's rate of travel as "x" mph. Since Chuck's rate of travel is 3 mph more than Dana's, we can denote Chuck's rate of travel as "x + 3" mph.
We know that Chuck traveled 236 miles and Dana traveled 224 miles. We also know that they traveled for the same amount of time.
Using the formula for both Dana and Chuck, we can write two equations:
224 = x * T
236 = (x + 3) * T
Now we can solve this system of equations to find the value of x, and thereby determine Chuck's rate of travel.
Let's eliminate the T variable by multiplying the first equation by (x + 3) and the second equation by x:
224(x + 3) = 236x
Expanding this equation:
224x + 672 = 236x
Next, isolate the x term by subtracting 224x from both sides:
672 = 12x
Now, divide both sides by 12 to solve for x:
x = 672/12
x = 56
Therefore, Dana's rate of travel is 56 mph.
To find Chuck's rate of travel, we substitute this value of x back into one of the original equations:
236 = (x + 3) * T
236 = (56 + 3) * T
236 = 59 * T
Finally, divide both sides by 59 to solve for T:
T = 236/59
T = 4
So, Chuck's rate of travel is 59 mph.