Question

An aircraft flew 5 hours with the wind . The return trip took 6 hours against the wind . If the speed of the plane in still air is 490 miles per hours more than the speed of the wind , find the wind speed and the speed of the plane in still air

Answer 1

Answer:

The speed of the plane in still air is 89.83 mph and the speed of air is 8.17 mph.

Step-by-step explanation:

Let the speed of the plane in still air is u mph and the speed of the wind is v mph.

Now, the aircraft flew 490 miles in 5 hours with the wind.  

Hence, $u + v = \frac{490}{5} = 98$ ........ (1)

Now, the aircraft flew 490 miles in 6 hours against the wind.

So, $u - v = \frac{490}{6} = 81.67$ ............ (2)

Now, adding equations (1) and (2) we get,

2u = 179.67

⇒ u = 89.83 mph

Now, from equation (1) we get,

v = 98 - u = 98 - 89.83 = 8.17 mph.

Therefore, the speed of the plane in still air is 89.83 mph and the speed of air is 8.17 mph. (Answer)