An airplane traveling east has a tailwind, and its speed is 550 + x mi/h. When the airplane flies west, it has a headwind and travels at 550 – x mi/h. If it takes 5 hours to travel from the West Coast to the East Coast of the United States and 6 hours to travel the same path from the East Coast to the West Coast, what is the value of x?
since distance = speed * time,
5(550+x) = 6(550-x)
so solve for x
50
To solve this problem, we will use the distance formula, which is:
Distance = Speed × Time
Let's consider the first scenario when the airplane is traveling from the West Coast to the East Coast.
Given that the speed of the airplane (with a tailwind) is 550 + x mi/h, and it takes 5 hours to travel, we can write:
Distance = (550 + x) × 5
Now, let's consider the second scenario when the airplane is traveling from the East Coast to the West Coast.
Given that the speed of the airplane (with a headwind) is 550 - x mi/h, and it takes 6 hours to travel, we can write:
Distance = (550 - x) × 6
Since the distance remains the same in both scenarios (traveling from one coast to the other), we can set these two expressions equal to each other:
(550 + x) × 5 = (550 - x) × 6
Expanding the equation:
2750 + 5x = 3300 - 6x
Bringing like terms to one side:
5x + 6x = 3300 - 2750
11x = 550
Dividing both sides by 11:
x = 50
Therefore, the value of x is 50.