A plane traveled for 5 hours witha tail wind of 12 mph. The return trip against the same wind took 10 hours. Find the speed of the plane in still air.

Question

ash2326 · Answer

Let the speed of plane be v
and speed of wind be u , it's given as 12mph
Let the distance it travels be x miles
so
With the wind it covers x in 5 hours
We have  distance= speed $\times$ time
with the wind speed of plane is (v+12)
$$x= (v+12) \times 5$$
against the wind it takes 10 hours
the speed of plane = v-12
so
$$x=(v-12) \times 10$$
Divide the two equations
we get
$$ 1=\frac{(v+12)\times 5}{(v-12)\times 10}$$
we get
now
$$10v-120=5v-60$$
$$5v=60$$
Speed of plane in still air
$$v= 24 mph$$

ash2326 · Answer

sorry made mistake at last
v= 12 mph

ash2326 · Answer

hello8 did you get it?

anonymous · Answer

yes sorry for late reply

anonymous · Answer

(I don't know why my PC rebels on me now)
Anyway:  v1 = v + 12,   v2 = v -12
5( v +12 ) = 10 (v- 12)
5v = 120 - 60 
-> v = 60/5 = 12 km/h