The Drive to Sue's Party
Featuring Bob and Tim
So what's the deal?
y = distance from Sue's house (km)
Bob and Tim's Drive to Sue's House: (graphed)
Equations in y-intercept form and standard form:
y = -60x + 50 or 60x + y - 50 = 0
y = -40x + 40 or 40x + y - 40 = 0
Finding the Point of Intersection:
-60x + 50 = -40x + 40
50 - 40 = -40x + 60x
10 = 20x
10 / 20 = x
0.5 = x
The P.O.I.'s x coordinate is 0.5. Now, to find the y value, we can sub in any of the equations to find y.
y = -60 (0.5) + 50
y = -30 + 50
y = 20
Hence, the P.O.I. is at (0.5, 20). This means that Bob would pass Tim after half an hour, with 20km left between them and Sue's house.
Conclusion and Significance
Bob and Tim are both 20km away from Sue's house at half an hour.
By solving this linear system, the following has become evident:
- From 0 minutes to 30 minutes, Tim is closer to Sue's house.
- At half an hour, Bob and Tim are both 20km away from Sue's house.
Bob would pass Tim after half an hour, with 20km left between them and Sue's house.
- After half an hour, Bob is closer to Sue's house.
We can also see that:
- Bob arrives at 0.83333333333333333 hours, which is at about 50 minutes.
- Tim arrives at exactly one hour.