SOLUTION: A car travels to and from a city 72 km away in 2 hours. If the average speed on the return trip is 30 km/h less than the trip to the city, what was the average speed of the car whe

Question 821037: A car travels to and from a city 72 km away in 2 hours. If the average speed on the return trip is 30 km/h less than the trip to the city, what was the average speed of the car when it was going toward the city?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
s = d / t
t = d / s
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to:
t = 72/s
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from:
t = 72/(s - 30)
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2 = 72/s + 72/(s - 30)
2 = 72(s - 30)/s(s - 30) + 72s/s(s - 30)
2s(s - 30) = 72(s - 30) + 72s
2ss - 60s = 72s - 2160 + 72s
2ss - 204s + 2160 = 0
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the above quadratic equation is in standard form, with a=2, b=-204, and c=2160
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 -204 2160
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
s = 90
s = 12
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the problem statement says that the speed of the return trip from the city is 30 kph slower than the speed towards the city, so the speed towards the city must be higher than 30 kph (so choose the root s=90)
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answer:
speed towards the city = 90 kph
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Solve quadratic equations, quadratic formula:
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---
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