Charlie and Violet met for lunch at a restuarant between their two locations (exactly in the middle). It took Charlie 2.6 hours to get there, but it only took Violet two hours because she was driving 15 mph faster than Charlie. The distance between the two of them intially was 260 miles. Find the speed of the two drivers.
To find the speed of the two drivers, let's work through the problem step by step.
Let's assume the speed at which Charlie is driving is "c" mph.
According to the problem, Violet is driving 15 mph faster than Charlie. So, her speed is "c + 15" mph.
We know that it took Charlie 2.6 hours to travel from his location to the restaurant. Violet, who was driving faster, took only 2 hours.
To find the distance each of them traveled, we can use the formula:
Distance = Speed × Time
For Charlie, the distance traveled is 2.6c miles.
For Violet, the distance traveled is 2(c + 15) miles.
Since they both met at the restaurant, the sum of the distances they traveled should be equal to the initial distance between them, which is 260 miles.
Therefore, we can write the equation:
2.6c + 2(c + 15) = 260
Let's solve this equation to find the value of "c" (Charlie's speed).
2.6c + 2c + 30 = 260
4.6c + 30 = 260
Now, let's isolate "c" by subtracting 30 from both sides:
4.6c = 260 - 30
4.6c = 230
Lastly, divide both sides by 4.6 to solve for "c":
c = 230 / 4.6
c = 50
So, Charlie's speed is 50 mph.
To find Violet's speed, we can just add 15 to Charlie's speed:
Violet's speed = 50 + 15 = 65 mph
Therefore, Charlie is driving at 50 mph, and Violet is driving at 65 mph.
Charlie' rate ---- x mph
Violet's rate = x+15 mph
You said they met at the midpoint, so didn't each go 130 miles ??
solve for x:
130/(x+15) = 2