Two planes flying opposite directions (north and south) pass each other 80 miles apart at the same altitude. The northbound plane is flying 200 mph (miles per hour) and the southbound plane is flying 150 mph. When are the planes 200 miles apart? (Round your answer to one decimal place.)
Let after t hours planes will be 500 miles apart.
Then EB = 200t BC = 150t
Therefore, EC = EB + BC = 350t
It's given that DC = 200 miles
By Pythagoras theorem again,
DC² = EC²+ DE²
(200)²= (350t)²+ (80)²
40000 = 122500t² + 6400
400=1225t² + 64
1225t² = 336
t² = 0.27438571 t=0.52 ≈ .52 hours = 31 mins
I have had people help and we all got this answer and when I put it in and check if it right it says that it wrong so can someone help me
Why are you switching names?
Read my last reply when you were Grant.
To find the time when the planes are 200 miles apart, we need to solve for t in the equation (200)²=(350t)²+(80)².
Starting from the equation:
40000 = 122500t² + 6400
Subtracting 6400 from both sides:
33600 = 122500t²
Dividing both sides by 122500:
0.2742857 = t²
Taking the square root of both sides:
t = √0.2742857
t ≈ 0.5235
So, the time when the planes are 200 miles apart is approximately 0.52 hours or 31 minutes.
It seems like you have the correct answer. However, if the system is not accepting it, there might be an issue with the input format or rounding. Double-check if the system requires the answer in a specific format (e.g., decimal or fraction) or if more decimal places are needed.
To find the time when the planes are 200 miles apart, we'll follow the steps you've mentioned:
1. Let's assume that after t hours, the planes will be 500 miles apart.
2. The distance covered by the Northbound plane in t hours is 200t (speed multiplied by time), and the distance covered by the Southbound plane is 150t.
3. Adding these distances, we get the total distance EC covered by both planes: EC = 200t + 150t = 350t.
4. From the given information, we know that DC (the initial distance between the planes) is 200 miles.
5. Using the Pythagorean theorem (DC² = EC² + DE²), we can set up the equation: 200² = (350t)² + 80².
6. Simplifying this equation, we have: 40000 = 122500t² + 6400.
7. Moving all terms to one side to form a quadratic equation: 122500t² = 33600.
8. Dividing both sides by 122500, we get: t² = 33600 / 122500.
9. Taking the square root of both sides, we find: t = sqrt(33600 / 122500).
10. Evaluating this expression, we get: t ≈ 0.27438571.
11. Now, the time t is in hours, but we need to convert it to minutes. Multiply t by 60 to convert it to minutes: t ≈ 0.27438571 * 60 ≈ 16.46 minutes.
12. Rounded to one decimal place, the planes are approximately 200 miles apart after 16.5 minutes (or 31 minutes when rounded to the nearest minute).
Please double-check your calculations to ensure you haven't made a mistake.