<h3>
Answer: 3240 miles</h3>
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Work Shown:
Convert the given speeds from "miles per hour" to "miles per minute"
540 mi/hr = (540 mi/hr)*(1 hr/60 min)
540 mi/hr = (540/60) (mi/min)
540 mi/hr = 9 mi/min
480 mi/hr = (480 mi/hr)*(1 hr/60 min)
480 mi/hr = (480/60) (mi/min)
480 mi/hr = 8 mi/min
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Let,
- d = distance between two airports
- x = time in minutes it takes the plane to travel 9 mi/min
- y = time in minutes it takes the plane to travel 8 mi/min
If the plane travels 9 mi/min, then,
distance = rate*time
d = 9*x
d/9 = x
x = d/9
Similarly if the plane travels 8 mi/min, then,
d = 8*y
d/8 = y
y = d/8
Subtract the time values y and x
y-x = d/8 - d/9
y-x = 9d/72 - 8d/72
y-x = (9d-8d)/72
y-x = d/72
This difference represents 45 minutes because 53 - 8 = 45. The 53 and 8 are from the fact the plane is late 53 minutes and 8 minutes.
In other words, y-x = 45, so d/72 = 45 which solves to d = 3240 when you multiply both sides by 72.
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Extra Info:
If d = 3240, then
x = d/9 = 3240/9 = 360
y = d/8 = 3240/8 = 405
So y-x = 405 - 360 = 45
If the plane travels 9 mi/min (aka 540 mph) then it spends 360 minutes (6 hours) doing so. If the plane travels 8 mi/min (480 mph) then it spends 405 minutes (6 hrs, 45 min) doing so. So this is a more detailed look at why the time gap is 45 minutes.
