SOLUTION: The Tour De France is a bicycle race that begins in Dublin,Ireland, but is primarily a race through France.On each day,racers cover a certain distance depending on the steepness of
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Question 63860This question is from textbook Intermediate Algebra with Applications
: The Tour De France is a bicycle race that begins in Dublin,Ireland, but is primarily a race through France.On each day,racers cover a certain distance depending on the steepness of terrian. Suppose that on one particular day, the racers must complete 210mi. One cyclist, traveling 10mph faster than a second cyclist, covers the distance in 2.4 hrs less time than the second cyclist. Find the rate of the first cyclist. This question is from textbook Intermediate Algebra with Applications
You can put this solution on YOUR website! the racers must complete 210 mi. One cyclist, traveling 10 mph faster than a second cyclist, covers the distance in 2.4 hrs less time than the second cyclist. Find the rate of the first cyclist.
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Let s = the speed of the 1st cyclist
Let (s-10) = speed of the 2nd cyclist
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Write a time equation: t = Dist/speed:
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1st cyclist time + 2.4 hr = 2nd cyclist time
210/s + 2.4 = 210/{s-10)
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Mult the equation by s(s-10) to get rid of the denominators:
210(s-10) + 2.4(s(s-10) = 210s
210s - 2100 + 2.4s^2 - 24s = 210s
2.4s^2 - 24s + 210s - 210s - 2100 = 0
2.4s^2 - 24s - 2100 = 0
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Solve for s using the quadratic equation: a=2.4, b = -24; c = -2100
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Do the math and you should get a positive solution of:
s = + 35 mph is the speed of the 1st cyclist
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Check solution using the time difference:
210/35 - 210/25 = 2.4 hrs
