A plane traveled 1794 miles to Bangkok and back. The trip there was with the wind. It took 13 hours. The trip back was into the
1 answer:
Answer:
The speed of wind is 30 miles/hour
Speed of plane in still air is 108 miles /hour
Step-by-step explanation:
Distance traveled by plane to Bangkok = 1794 miles
The trip there was with the wind. Time taken = 13 hours.
The trip back was into the wind. The trip back took 26 hours.
Let s = plane speed in still air
let w = speed of the wind
(s+w) = speed of plane with wind
(s-w) = speed of plane against wind
Distance = Speed * Time
When the trip was with the wind .
⇒
⇒
⇒ ---1
When The trip back was into the wind.
⇒
⇒
⇒ ---2
Add 1 and 2
⇒s+w+s-w =138+78
⇒2s =216
⇒
⇒
To find w substitute the value of s in 1
⇒
⇒
⇒
Thus the speed of wind is 30 miles/hour
Speed of plane in still air is 108 miles /hour
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Finding the discriminant:
The roots of a quadratic equation are real and distinct if the value of its discriminant is greater than 0.
If we observe the value of discriminant, it is a sum of two terms in this case. The first term is square of (5h), which will always be a positive term or zero if h is zero. The second term is 24k. The value of 24k will always be positive for positive values of k.
Thus for positive values of k, the discriminant of given equation is always positive and thus we can say the root of given equation will always be real and distinct for positive values of k.