Final answer:
To reach Luna's house at the same time as her, Ron, who leaves 30 minutes after Luna, must travel at a speed of 5 km/h to cover the 10 km distance in the remaining 2 hours.
Step-by-step explanation:
Calculating Ron's Required Speed to Reach Luna's House
Luna leaves her school at 1:35 p.m. and travels to her home 10 km away at a speed of 4 km/h. To find out how quickly Ron has to fly to get to Luna's house at the same time, we first determine the time it will take Luna to reach her home. Traveling at 4 km/h for 10 km gives Luna a travel time of 2.5 hours (since time = distance ÷ speed, which is 10 km ÷ 4 km/h).
Luna is expected to arrive home at 4:05 p.m. (since 1:35 p.m. + 2.5 hours = 4:05 p.m.). Ron leaves 30 minutes later than Luna, which means he sets off at 2:05 p.m. To arrive at the same time as Luna, Ron must cover the 10 km distance in the remaining 2 hours (4:05 p.m. - 2:05 p.m.).
To calculate the speed Ron needs to travel at, we use the formula speed = distance ÷ time. Plugging in the values gives us speed = 10 km ÷ 2 hours, which results in a required speed of 5 km/h for Ron.