A jet plane traveling at 550 mph overtakes a propeller plane traveling at 150 mph that had a 22-hour head start. How far from the starting point are the planes?
The planes are ____ miles from the starting point.
the closing speed is 400 mph (550 - 150)
the 22 hr head start at 150 mph is 3300 mi
time to catch up is ... 3300 mi / 400 mph
catch up distance is
... (catch up time) * 550 mph
To find the distance from the starting point where the planes are, we need to determine the distance each plane has traveled.
Let's start with the propeller plane. It had a 22-hour head start and is traveling at a speed of 150 mph. Therefore, in 22 hours, the propeller plane would have traveled (22 hours) x (150 mph) = 3,300 miles.
Now, let's consider the jet plane. It is traveling at a speed of 550 mph and overtakes the propeller plane. Since the jet plane is faster, it will catch up to and overtake the propeller plane at a certain point. The time it takes for the jet plane to catch up to the propeller plane can be calculated by dividing the distance between them (3,300 miles) by the speed difference (550 mph - 150 mph = 400 mph). Therefore, the catching up time is (3,300 miles) / (400 mph) = 8.25 hours.
Now, let's calculate the distance the jet plane has traveled in 8.25 hours. The distance traveled can be found by multiplying the catching up time by the speed of the jet plane, which is (8.25 hours) x (550 mph) = 4,537.5 miles.
So, the distance from the starting point where the planes are is 4,537.5 miles.