can you help in math?
An airline runs a commuter flight between Portland, Oregon, and Seattle, Washington, which are 145 miles apart. if the average speeed 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?
Mathematics - 1 Answers
Random Answers, Critics, Comments, Opinions :
1 :
x = current average speed (miles per hour) x + 40 = proposed average speed (miles per hour) t = current travel time (hours) t - 12/60 = proposed travel time (hours) 145 = tx => t = 145/x 145 = (t - 0.2)(x + 40) = tx + 40t - 0.2x - 8 145 = tx + 40t - 0.2x - 8 = tx cancel the "tx" terms: 40(145/x) - 0.2x - 8 = 0 multiply by "x": 5800 - 0.2x² - 8x = 0 divide by "-0.2" and rearrange: x² + 40x - 29000 = 0 solve for x via the quadratic formula: x = -20 ± √(400 + 29000) = -20 ± 171.5 ignore the negative root as being outside the domain: x = 151.5 The average speed of the plane is currently 151.5 mph. The proposed increased speed is 191.5 mph. Verification: Current flight time = 145/151.5 = .957 hours = 57.4 minutes Proposed flight time = 145/191.5 = .757 hours = 45.4 minutes Time differential = 57.4 - 45.4 = 12 minutes
