3.Two planes leave an airport flies at the same rate.if the first plane flies 1, :5 hours longer than

Question

the second plane and travels 2700 miles while the second plane travels only 2025 miles, for how
long was each plane flies?

Answer 1

Let's denote the flying rate of both planes as \( r \) (in miles per hour).

Let \( t \) be the time the second plane flies. Then, the first plane flies for \( t + 1.5 \) hours.

From the problem, we have the following equations for distance:

For the first plane: \[ \text{Distance} = \text{Rate} \times \text{Time} \] \[ 2700 = r(t + 1.5) \]

For the second plane: \[ 2025 = rt \]

Now we have two equations:

1. \( 2700 = r(t + 1.5) \)
2. \( 2025 = rt \)

We can solve for \( r \) from the second equation: \[ r = \frac{2025}{t} \]

Now substitute \( r \) into the first equation: \[ 2700 = \left(\frac{2025}{t}\right)(t + 1.5) \] \[ 2700 = 2025 \left(1 + \frac{1.5}{t}\right) \] \[ 2700 = 2025 + \frac{2025 \times 1.5}{t} \] \[ 2700 - 2025 = \frac{2025 \times 1.5}{t} \] \[ 675 = \frac{3037.5}{t} \] \[ t = \frac{3037.5}{675} \] \[ t = 4.5 \text{ hours} \]

Now, to find the time for the first plane: \[ t + 1.5 = 4.5 + 1.5 = 6 \text{ hours} \]

Thus, the second plane flies for 4.5 hours and the first plane flies for 6 hours.