Pre-calculus experts, please help me on this!!!?
An airline runs a commuter flight between Portland, Oregon and Seattle, Washington, which are 145 miles apart. If the average speed of the plane could be increased by 40 miles per hour, the travel time would be decreased by 12 minutes. What airspeed is required to obtain this decrease in travel time? Round your result to one decimal place.
Mathematics - 2 Answers
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1 :
let higher air speed be x mph, lower speed = x-40 mph, time at higher speed = t hrs, at lower speed = t+1/5 hrs at higher speed, xt = 145 or t = 145/x set-up equation using slower speed (x-40)(145/x +1/5) = 145 expand into a quadratic, solve & take +ve value ans: x = 191.46 => 191.5 mph ------
2 :
Original speed—x: y = 145/x y - 12/60 = 145/(x + 40) y - 1/5 = 145/(x + 40) 5y - 1 = 725/(x + 40) 5xy + 200y - x - 40 = 725 5xy + 200y = x + 765 y(5x + 200) = x + 765 y = (x + 765)/(5x + 200) 145(5x + 200) = x(x + 765) 725x + 29,000 = x² + 765x x² + 20x = 29,000 + 20² x² + 20x = 29,000 + 400 (x + 20)² = 29,400 x + 20 = 171.464282 x = 151.464282 Required speed: = 151.464282 + 40 = 191.464282 Answer: 191.5 mph is the required speed to obtain the decrease in travel time. Proof: = 60(145/151.5 - 145/191.5 hrs) = 60(0.957 - 0.757 hrs) = 60(0.2 hrs) = 12 minutes
