pilot flies 512 miles against a 22-mile-per-hour wind. On the next day, the pilot flies back home with a 12-mile-per-hour tail wind. The total trip (both ways) takes 4 hours. Find the speed of the airplane without a wind.

[tex]\frac{512}{V_p-22}+\frac{512}{V_p-12}=4\\\Rightarrow 512\left(V_p+12\right)+512\left(V_p-22\right)=4\left(V_p-22\right)\left(V_p+12\right)\\\Rightarrow 4V_p^2-1064V_p+4064=0[/tex]

Solving this quadratic equation we get,

[tex]V_p=\frac{-\left(-1064\right)+\sqrt{\left(-1064\right)^2-4\cdot \:4\cdot \:4064}}{2\cdot \:4}, \frac{-\left(-1064\right)-\sqrt{\left(-1064\right)^2-4\cdot \:4\cdot \:4064}}{2\cdot \:4}\\\Rightarrow V_p=262.12367, 3.87[/tex]

So, velocity of boat in plane without wind is 262.12367 mph

pilot flies 512 miles against a 22​-mile-per-hour wind. On the next​ day, the pilot flies back home with a 12​-mile-per-hour tail wind. The total trip​ (both ways) takes 4 hours. Find the speed of the airplane without a wind.

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pilot flies 512 miles against a 22-mile-per-hour wind. On the next day, the pilot flies back home with a 12-mile-per-hour tail wind. The total trip (both ways) takes 4 hours. Find the speed of the airplane without a wind.