A train traveling at a constant speed takes a passenger from Deer Lake to Liberty, stopping first at Summerville and next at Cyp
ress before arring at Liberty. It takes three times as long to go from Deer Lake to Summerville as it does to go from Summerville to Cypress. It takes twice as long to go from Cypress to Liberty as it does to go from Summerville to Cypress. How far is the ride from Deer Lake to Cypress if the entire trip is 360 miles? Name a geometric postulate or theorem used to find the solution.
2 answers:
Answer:
The ride from Deer Lake to Cypress is 240 [mi]. To find the solution we use the segment addition postulate
Explanation:
The segment addition postulate states that for a line with initial point A and finish point C, a third point B lies in the segment only if the distances between points satisfies the following equation:
- AB + BC = AC
In this case, we have a line with four points:
A - Deer Lake
B - Summerville
C - Cypress
D - Liberty
And we are required to find the distance from Deer Lake to Cypress (AC) knowing that AD = 360 [mi] and knowing that:
- AD = AB + BC + CD --> This is the equation derived from the segment addition postulate.
- AB = 3BC --> Going from Deer Lake to Summerville takes three times as long than going from Summerville to Cypress. Since the speed is constant, three times the time means three times the distance.
- CD = 2BC --> (Same expalantion as above, except for different locations)
We end up with 3 equations and 3 unknowns. All we need to do now is to solve it
- Substitue equation 2 and 3 in equation 1 and solve for BC
- Use equation 2 to get AB
- Use equation 3 to get BC
They want us to find AC (Deer Lake to Cypress), we knoe the postulate, we know the values:
- AC = AB + BC = 180 + 60
- AC = 240 [mi]
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