A jet liner flying east with the wind traveled 3600 km in 6 hours. The return trip, flying against the wind, took 8 hours. Find the rate at which the jet flew in still air and the... A jet liner flying east with the wind traveled 3600 km in 6 hours. The return trip, flying against the wind, took 8 hours. Find the rate at which the jet flew in still air and the rate of the wind. Read more

Steps to Solve

1. Define Variables Let $j$ be the speed of the jet in still air (in km/h) and $w$ be the speed of the wind (in km/h).

2. Set Up Equations for the Outbound Trip The jet traveled 3600 km with the wind in 6 hours. Using the formula:

$$ \text{Distance} = \text{Speed} \times \text{Time} $$

The speed going east (with the wind) is:

$$ j + w = \frac{3600 \text{ km}}{6 \text{ hours}} = 600 \text{ km/h} $$

So, the first equation is:

$$ j + w = 600 \tag{1} $$

3. Set Up Equations for the Return Trip On the return trip, the jet flew against the wind and took 8 hours. The speed going back is:

$$ j - w = \frac{3600 \text{ km}}{8 \text{ hours}} = 450 \text{ km/h} $$

So, the second equation is:

$$ j - w = 450 \tag{2} $$

4. Solve the System of Equations Now, we will solve the two equations:

From equation (1):

$$ j + w = 600 $$

From equation (2):

$$ j - w = 450 $$

Adding these two equations together:

$$ (j + w) + (j - w) = 600 + 450 $$

This simplifies to:

$$ 2j = 1050 $$

Then, divide by 2:

$$ j = 525 \text{ km/h} $$

5. Find the Speed of the Wind Now substitute $j = 525$ back into equation (1):

$$ 525 + w = 600 $$

Subtract 525 from both sides:

$$ w = 75 \text{ km/h} $$