Question

a commercial jet can fly 1,728 miles in 4 hours with a tailwind but only 1,530 miles in 5 hours into a headwind. find the speed of the jet in still air and the speed of the wind. select one: a. jet 375 mph and wind 60 mph. b. jet 369 mph and wind 70 mph. c. jet 360 mph and wind 75 mph. d. jet 369 mph and wind 63 mph.

Explanation:

Step1: Define variables

Let $j$ = jet speed in still air (mph), $w$ = wind speed (mph).

Step2: Calculate ground speeds

Tailwind speed: $\frac{1728}{4}=432$ mph, so $j + w = 432$.
Headwind speed: $\frac{1530}{5}=306$ mph, so $j - w = 306$.

Step3: Solve for $j$

Add the two equations:
$$(j + w) + (j - w) = 432 + 306$$
$$2j = 738$$
$$j = \frac{738}{2}=369$$

Step4: Solve for $w$

Substitute $j=369$ into $j + w = 432$:
$$369 + w = 432$$
$$w = 432 - 369=63$$

Answer:

D. Jet 369 mph and wind 63 mph.