Two planes leave an airport flying at the same rate. If the first
plane flies 1.5 hours longer than the second plane and travels 2700
miles while the second plane travels only 2025 miles, for how long
was each plane flying?
Let x be the time (in hours) the second plane was flying.
Since the first plane flew 1.5 hours longer than the second plane, the first plane was flying for x + 1.5 hours.
The speed of both planes is the same, so we can set up the equation:
2700 = (x + 1.5) * speed
2025 = x * speed
Divide the first equation by the second equation to find the value of speed:
2700 / (x + 1.5) = 2025 / x
2700x = 2025(x + 1.5)
2700x = 2025x + 3037.5
675x = 3037.5
x = 4.5
The second plane was flying for 4.5 hours, and the first plane was flying for x + 1.5 = 4.5 + 1.5 = 6 hours.