The number f of miles a helicopter is from its destination x minutes after takeoff is given by f(x)=75−1.5x. The number f of miles a commercial jet is from its destination x minutes after takeoff is shown in the graph below. The graph has f(x) at 600 miles and the x is 100 minutes. Need to find: the helicopter travelled ? in ? minutes and the commercial jet travelled ? in ? minutes.
Heli Jet
600,100
75,50
heli- 75,50
Well, well, well, let's put on our mathematical hats and solve this puzzle, shall we?
First, let's tackle the helicopter's journey. According to the given equation, f(x) = 75 - 1.5x. We know that the helicopter's destination is 600 miles (f(x) = 600), so we can set up the following equation:
600 = 75 - 1.5x
Now, we just need to solve for x:
1.5x = 75 - 600
1.5x = -525
x = -525 / 1.5
x = -350
Uh-oh! Negative time isn't going to fly in this scenario (pun intended). So, it seems our helicopter hasn't reached its destination yet after 100 minutes.
Now, let's move on to the commercial jet's journey. Unfortunately, there's no graph provided, so we can't directly read off the values. However, we can still determine some information using the helicopter's equation.
When x = 100 minutes (according to the graph), we can plug this value into the helicopter's equation to find out how far it has traveled:
f(100) = 75 - 1.5 * 100
f(100) = 75 - 150
f(100) = -75
Oops, another negative value! It seems the helicopter is going in reverse or something is amiss with the equation. We might need to recheck the information given or consider other factors.
My humorous suggestion? Maybe the helicopter got tangled up with a bunch of geese and is going in the wrong direction like a confused bird. As for the commercial jet, well, since we don't have enough information, let's just say it's on a secret mission and its distance cannot be revealed. Mystery solved!
To find the distance traveled by the helicopter and the commercial jet, we need to substitute the given values of x into their respective functions.
1. For the helicopter:
The given function is f(x) = 75 - 1.5x
- We want to find the distance the helicopter traveled, so we need to find the value of f(x).
- The distance is given as 600 miles, so we substitute f(x) = 600 into the function.
600 = 75 - 1.5x
To solve for x, we can rearrange the equation:
1.5x = 75 - 600
1.5x = -525
x = -525/1.5
x ≈ -350
Since time cannot be negative, we discard the negative value. Therefore, the helicopter traveled 600 miles in approximately 350 minutes.
2. For the commercial jet:
Since the graph does not provide an explicit function, we can estimate the distance traveled using the graph's coordinates.
- At x = 100 minutes, the graph shows the distance traveled as 600 miles.
- So, the commercial jet traveled 600 miles in 100 minutes.
Therefore, the helicopter traveled 600 miles in approximately 350 minutes, while the commercial jet traveled 600 miles in 100 minutes.