SOLUTION: Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables. John

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Question 295877: Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
John and Tony start from the same place at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find the speed of each.
Answer by stanbon(75887) (Show Source):
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John and Tony start from the same place at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find the speed of each.
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Let t = Tony's time ; Let j = John's time
Time Equation: t-j = 3
Rate Equation: 10/j = 2(10/t)
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Solve the Time Eq. for t: t = j+3
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Substitute for "t" in the Rate Equation and solve for "j":
10/j = 2(10/(j+3))
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1/j = 2/(j+3)
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j+3 = 2j
j = 3 hrs (John's time)
t = 6 hrs (Tony's time)
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John's speed = 10/3 mph
Tony's speed = 10/6 mph
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Cheers,
Stan H.
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