Question 934632
x = speed on first part
y = speed on second part
x = y + 20
y = x - 20
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s = d/t
t = d/s
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time on first part:
t = time on first part
t = 160/x
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time on second part:
4 - t = 80/y
4 - t = 80/(x - 20)
t = 4 - 80/(x - 20)
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equate times:
160/x = 4 - 80/(x - 20)
160/x + 80/(x - 20) = 4
160(x - 20)/x(x - 20) + 80x/x(x - 20) = 4
160(x - 20) + 80x = 4x(x - 20)
160x - 3200 + 80x = 4xx - 80x
4xx - 80x - 80x - 160x + 3200 = 0
4xx - 320x + 3200 = 0
xx - 80x + 800 = 0
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the above quadratic equation is in standard form, with a=1, b=-80 and c=800
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -80 800
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the quadratic has two real roots at:
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x = 68.2842712
x = 11.7157288
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the root x=11.7 would make y negative, which doesn't fit the problem statement, so use the first root:
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answer:
x = speed on first part = 68.2842712 mph
y = speed on second part = 48.2842712 mph
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