SOLUTION: A hydrofoil made a round-trip of 144 km in 4 hours. because of headwinds the average speed on returning was 15 km/h less than the average speed going out. find both individual spe

Question 928955: A hydrofoil made a round-trip of 144 km in 4 hours. because of headwinds the average speed on returning was 15 km/h less than the average speed going out. find both individual speeds (going out and returning)
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = speed outbound
speed inbound = x - 15
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y = time outbound
z = time inbound
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w = distance of one leg (outbound or inbound) = 144/2 = 72 km
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s = d/t
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outbound:
x = w/y
x = 72/y
y = 72/x
---
inbound:
x - 15 = w/z
x - 15 = 72/z
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total time:
y + z = 4
---
y + z = 4
y = 72/x
72/x + z = 4
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72/x + z = 4
z = 4 - 72/x
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x - 15 = 72/z
z(x - 15) = 72
z = 4 - 72/x
(4 - 72/x)(x - 15) = 72
4x - 60 - 72 + 1080/x = 72
x(4x - 132 + 1080/x = 72)
4xx - 132x + 1080 = 72x
4xx - 204x + 1080 = 0
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the above quadratic equation is in standard form, with a=4, b=-204 and c=1080
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
4 -204 1080
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 45
x = 6
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the root x=6 doesn't fit the problem statement, as it forces the speed inbound (x-15) to be negative, so use the root x=45:
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answer:
x = speed outbound = 45 kph
speed inbound = x-15 = 30 kph
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Solve quadratic equations, quadratic formula:
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---
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