An Air Force jet is going on a long-distance flight and will need to be refueled in midair over the Pacific Ocean. A refueling plane that carries fuel can travel much farther than the jet but flies at a slower speed. The refueling plane and jet will leave from the same base, but the refueling plane will leave 3 hours before the jet. The jet will fly at 800 mph and the refueling plane will fly at 530 miles per hour. a) How long after the jet takes off will the two planes meet? b) How far from the base will the refueling take place? a) How long after the jet takes off will the two planes meet? 5.8889 hours (Type an integer or decimal rounded to four decimal places as needed.) b) How far from the base will the refueling take place? miles (Type an integer or decimal rounded to two decimal places as needed.)

To solve this problem, we can break it down step by step. The refueling plane takes off 3 hours early, and the jet takes off later. 1. **Calculating the time until they meet (from jet’s take-off):** Let \( t \) be the time (in hours) the jet is flying when they meet. By the time the jet takes off, the refueling plane has already been flying for 3 hours. Therefore, the refueling plane has been flying for \( t + 3 \) hours when they meet. Using the distance formula (Distance = Speed × Time), we can set up two equations based on their distances from the base: - Distance of the jet: \( 800t \) - Distance of the refueling plane: \( 530(t + 3) \) Since they will have traveled the same distance when they meet: \[ 800t = 530(t + 3) \] Expanding the equation: \[ 800t = 530t + 1590 \] \[ 800t - 530t = 1590 \] \[ 270t = 1590 \] \[ t = \frac{1590}{270} \approx 5.8889 \text{ hours} \] So, the time after the jet takes off when they meet is approximately \( 5.8889 \) hours. 2. **Calculating the distance from the base where refueling takes place:** Now we plug \( t \) back into the distance equation for the jet: Distance where refueling occurs (from the base) is: \[ 800t = 800 \times 5.8889 \] \[ \approx 4709.12 \text{ miles} \] So, they will meet approximately \( 4709.12 \) miles from the base for the refueling. Thus, the final answers are: a) \( 5.8889 \) hours b) \( 4709.12 \) miles