Christine lives in Bangor, Maine , and her friend Denise Brown lives in Sioux City, Iowa. They both drive to Dade City, Florida, for the winter. The trip is 1600 miles for Christine and 1500 miles for Denise. If Christine drives 5 miles per hour faster than Denise, and if they take the same amount of time to complete the trip, determine the rate for Christine and the rate for Denise.
since time = distance/speed, and Christine's speed is c,
1600/c = 1500/(c-5)
c = 80
To determine the rates for Christine and Denise, we need to set up a system of equations based on the given information.
Let's say the rate for Denise is x miles per hour. Since Christine drives 5 miles per hour faster than Denise, her rate would be x + 5 miles per hour.
Now we can use the formula: distance = rate × time to set up equations for both Christine and Denise.
For Christine:
1600 miles = (x + 5) miles per hour × time
For Denise:
1500 miles = x miles per hour × time
Since they both take the same amount of time to complete the trip, we can set the equations equal to each other:
(x + 5) miles per hour × time = x miles per hour × time
Now we can cancel out the "time" variable on both sides since it's the same for both equations:
x + 5 = x
Solving the equation:
x - x = -5
0 = -5
We ended up with a contradiction, which means there is no solution to this problem. It seems there may be an error or inconsistency in the given information.