Jim is a paratrooper who has to land on a moving aircraft carrier. If his plane is flying with 90 miles per hour, he will be an hour early for the intercross. If his plane travels at a speed of 80 miles per hour, he will be an hour late for landing on the ship. How long is Jim’s scheduled flight-time?
since distance = speed * time,
90(t-1) = 80(t+1)
To solve this problem, we can use the concept of relative velocity. Let's break down the information given:
1. When Jim's plane is flying at 90 miles per hour, he arrives one hour early.
2. When Jim's plane is flying at 80 miles per hour, he arrives one hour late.
Let's assume that Jim's scheduled flight time is "t" hours.
With these assumptions, we can calculate the relative velocity between Jim's plane and the aircraft carrier in both cases:
1. When Jim is one hour early:
- Jim's plane is moving at 90 miles per hour.
- The relative velocity between the plane and the aircraft carrier is 90 miles per hour.
2. When Jim is one hour late:
- Jim's plane is moving at 80 miles per hour.
- The relative velocity between the plane and the aircraft carrier is -80 miles per hour (since the plane is moving slower than the carrier).
Now, we need to find out how far apart the plane and the aircraft carrier are at the scheduled flight time "t". We can use the formula:
Distance = Relative Velocity × Time
With the relative velocities obtained from the given information, we can calculate the distance in both cases:
1. Jim arrives one hour early:
Distance = 90 miles/hour × (t - 1) hours
2. Jim arrives one hour late:
Distance = -80 miles/hour × (t + 1) hours
Since the distance is the same in both cases (Jim always has to land on the aircraft carrier), we can set these two equations equal to each other:
90(t - 1) = -80(t + 1)
Now, let's solve this equation to find the value of "t", which represents Jim's scheduled flight time.