This is the complete question;
A plane traveled 580 miles to its destination and then returned home. The trip there was with the wind. It took 5 hours. The trip back was into the wind. The trip took 10 hours. Find the speed of the plane in still air and the speed of the wind
Answer:
Speed of plane in still air = 116 miles/hr
Speed of wind = 87 miles/hr
Step-by-step explanation:
Let the speed of the plane in still air be p
Let the speed of the wind be w
Now, we know that speed = distance/time.
Thus, on the trip going, the time was spent was 5 hours while the distance is 580 miles.
Thus, the total speed on this trip going is; 580/5 = 116 miles/hr
Now, the question says this trip was with the wind. Thus it means the plane speed and wind speed aided the movement.
So, p + w = 116 miles/hr - - - - - (eq1)
Now, on the return trip of 10 hours , it says plane was into the wind which means plane speed minus wind speed.
Thus,
p - w = 580/10
p - w = 58 miles/hr - - - - - (eq2)
Add eq 1 to eq 2 to get ;
2p = 116 + 58
2p = 174
p = 87 miles/hr
Plug in this into eq 2 to get
87 - w = 58
w = 87 - 58 = 29 miles/hr
