SOLUTION: Tatiana takes a 40 mile round trip bicycle trip and travels at a a constant speed the entire. On the first leg of the trip, she is riding against the wind, which is blowing at a co

Question 872957: Tatiana takes a 40 mile round trip bicycle trip and travels at a a constant speed the entire. On the first leg of the trip, she is riding against the wind, which is blowing at a constant rate of 3 miles per hour. On her return trip, she is riding with the wind. She starts the bike ride at 11:30 am and ends at 3:30 pm. How fast would Tatiana ride her bike on an absolutely windless day? If necessary, round your answers to the nearest hundredth.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Tatiana takes a 40 mile round trip bicycle trip and travels at a a constant speed the entire. On the first leg of the trip, she is riding against the wind, which is blowing at a constant rate of 3 miles per hour. On her return trip, she is riding with the wind. She starts the bike ride at 11:30 am and ends at 3:30 pm. How fast would Tatiana ride her bike on an absolutely windless day? If necessary, round your answers to the nearest hundredth.
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1st leg DATA:
dist = 20 miles ; rate = r-3 mph ; time = d/r = 20/(r-3) hrs
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2nd leg DATA:
dist = 20 miles ; rate = r+3 mph ; time = d/r = 20/(r+3) hrs
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Equation:
time + time = 4 hrs
20/(r-3) + 20/(r+3) = 4
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20(r+3) + 20(r-3) = 4(r^2-9)
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40r = 4r^2 - 36
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r^2 - 10r - 9 = 0
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r = [10 +- sqrt(100-4*-9)]/2
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r = [10 +- sqrt(136)]/2
Positive solution:
r = 10.83 mph (rate in still air)
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Cheers,
Stan H.
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