SOLUTION: To get to work Sam jogs 3 kilometers to the train, then rides the remaining 5 kilometers. If the train goes 40 km per hour faster than Sam's constant rate of jogging and the enti
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Question 103605This question is from textbook Precalculus
: To get to work Sam jogs 3 kilometers to the train, then rides the remaining 5 kilometers. If the train goes 40 km per hour faster than Sam's constant rate of jogging and the entire trip takes 1/2 hour how fast does Sam jog? This question is from textbook Precalculus
You can put this solution on YOUR website! To get to work Sam jogs 3 kilometers to the train, then rides the remaining 5 kilometers. If the train goes 40 km per hour faster than Sam's constant rate of jogging and the entire trip takes 1/2 hour how fast does Sam jog?
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Let s = his jogging speed
then
(s+40) = train speed
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Write a time equation: Time = Distance/speed
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jog time + train time = .5 hrs + = .5
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Multiply equation by s(s+40) and you have:
3(s+40) + 5s = .5(s(s+40))
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3s + 120 + 5s = .5s^2 + 20s
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8s + 120 = .5s^2 + 20s
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0 = .5s^2 + 20s - 8s - 120
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.5s^2 + 12s - 120 = 0; a quadratic equation
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Use the quadratic formula to find s: a=.5; b=12; c=-120
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s = -12 + 19.5959; we only need the positive solution here
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s = +7.5959 km/hr is his jogging speed
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Check solution by finding the time + =
.394 + .105 = .499 ~ .5 hrs
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