in a balloon race,the sum of the distances covered by two of the balloons was 1,025 miles.if the distance covered by the first balloon was 50 miles more than 1/2 of that covered by the second balloon,how far did each travel?
To solve this problem, we'll set up a system of equations. Let's call the distance covered by the second balloon "x" (in miles).
According to the problem, the distance covered by the first balloon is 50 miles more than half of that covered by the second balloon. So, the distance covered by the first balloon is (1/2)x + 50 miles.
We also know that the sum of the distances covered by both balloons is 1,025 miles. Therefore, the equation can be written as:
x + (1/2)x + 50 = 1,025
Now, let's solve this equation to find the value of x, which represents the distance covered by the second balloon.
Combining like terms, we have:
(3/2)x + 50 = 1,025
Subtracting 50 from both sides, we get:
(3/2)x = 975
Dividing both sides by (3/2), we find:
x = (975 รท (3/2)) = 650
Therefore, the distance covered by the second balloon is 650 miles.
To find the distance covered by the first balloon, we can substitute the value of x back into the equation:
Distance covered by the first balloon = (1/2)x + 50 = (1/2)(650) + 50 = 325 + 50 = 375
So, the distance covered by the first balloon is 375 miles, and the distance covered by the second balloon is 650 miles.