Question

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.

Answer 1

262.12367 mph

Step-by-step explanation:

`V_a` = Velocity of air

`V_p` = Velocity of plane

Distance to travel = 512 km

Total time taken = 4 hours

So,

`(512)/(V_p-22)+(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`

Solving this quadratic equation we get,

`V_p=(-\left(-1064\right)+√(\left(-1064\right)^2-4\cdot \:4\cdot \:4064))/(2\cdot \:4), (-\left(-1064\right)-√(\left(-1064\right)^2-4\cdot \:4\cdot \:4064))/(2\cdot \:4)\\\Rightarrow V_p=262.12367, 3.87`

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