SOLUTION: To reach a vacation spot, the Jones family first traveled by plane and then drove the remaining distance in a rented car. The distance by car was 125 Kilometers less than the dist

Algebra ->  Coordinate-system -> SOLUTION: To reach a vacation spot, the Jones family first traveled by plane and then drove the remaining distance in a rented car. The distance by car was 125 Kilometers less than the dist      Log On


   

Question 71220: To reach a vacation spot, the Jones family first traveled by plane and then drove the remaining distance in a rented car.
The distance by car was 125 Kilometers less than the distance by plane. The total distance was 500 kilometers less than three times the distance traveled by car, find the distance flown in the airplane.
HELP!!
Dorothy
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The distance by car was 125 Kilometers less than the distance by plane. The total distance was 500 kilometers less than three times the distance traveled by car, find the distance flown in the airplane.
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Let the plane distance be "x" miles.
Then the car distance is "x-125".
EQUATION:
x+ x-125 = 500
2x = 625
x = 312.5 miles (plane distance)
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Cheers,
Stan H.
12

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!

Let P be the distance traveled by plane and C be the distance traveled by car.
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The first sentence says that the distance traveled by car is 125 Km less that the distance traveled by plane. In equation form this can be written:
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C = P - 125 Km
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The total distance traveled is the sum of the distance traveled by plane (P) plus the distance traveled by car (C). But the second sentence says that this total distance is 500 Km less than 3 times the distance traveled by car. In equation form we can write:
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Total distance = 3*C - 500
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But we already said that Total Distance = P + C. So let's substitute P + C for "Total distance" to get the equation:
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P + C = 3*C - 500
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This equation can't be solved because it has 2 unknowns. A linear equation can be solved only if it has just unknown. So we need to get rid of one of the unknowns. To do this we return to the previous equation we wrote ... the equation:
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C = P - 125 Km
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What happens if we substitute the right side of this equation into the equation:
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P + C = 3*C - 500
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So for every C in this we plug in P - 125. When we do we get:
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P + (P - 125) = 3*(P - 125) - 500
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On the left side the parentheses are preceded by a plus sign so we can just remove them with out any changes. On the right side we need to multiply 3 times the 2 terms in parentheses. When we do these two things we get:
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P + P - 125 = 3P - 375 - 500
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Add the 2 P's on the left side and combine the - 375 and - 500 on the right side to get:
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2P - 125 = 3P - 875
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Subtract 3P from both sides to remove the 3P from the right side:
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-P - 125 = - 875
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Next add +125 to both sides to get rid of the 125 on the left side. When you do the equation becomes:
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-P = -750
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Multiply both sides by -1 and you finally end up with the answer to the problem:
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P = 750 Km
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Check. C = 750 - 125 = 625 Km
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Total distance equals 3*C - 500 = 3*625 - 500 = 1875 - 500 = 1375
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But total distance is C + P = 625 + 750 = 1375
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Everything seems to check.
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Hope this helps you to understand the problem better.