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?
let the distance be d miles
time at 90 mph = d/90
time at 80 mph = d/80
d/80 - d/90 = 1
times 720
9d - 8d = 720
d = 720 miles
good answer, but it does not address the question.
an hour early and an hour late means there are two hours inbetween, so:
d/80 - d/90 = 2 times 720
9d - 8d = 1440
d = 1440 miles and takes 17 hours
To find Jim's scheduled flight time, we can set up a system of equations using the given information. Let's denote Jim's scheduled flight time as "t" (in hours).
From the first part of the problem, we know that if Jim's plane is flying at 90 miles per hour, he will be an hour early for the rendezvous. This means that he covers the distance between the take-off point and the aircraft carrier in t - 1 hours. Since his plane is flying at a speed of 90 miles per hour, we can write the equation:
Distance = Speed × Time
90(t - 1) = Distance
From the second part of the problem, we know that if Jim's plane is flying at 80 miles per hour, he will be an hour late for landing on the ship. This means that he covers the same distance in t + 1 hours. Using the same formula, we can write the equation:
80(t + 1) = Distance
Since the distance covered is the same in both cases, we can set the two equations equal to each other:
90(t - 1) = 80(t + 1)
Now we can solve for t:
90t - 90 = 80t + 80
10t = 170
t = 17
Therefore, Jim's scheduled flight time is 17 hours.