An airline runs a commuter flight between Portland and Seattle, which are 145 miles apart. If the average air speed could be increased by 40 miles per hour, the travel time would be decreased by 12 minutes. What air speed is required to obtain this decrease in travel time?

Question

-I know I have to set up equations and use the quadratic equation, however I don't know how to do this. I believe the answer should be 190. Thanks for any help in advance!

Answer 1

Just think about what you have and what you need.

distance (miles) is speed(mi/hr) * time (hr)
If t is the current travel time, and s is the current speed, then

st = 145
t = 145/s

At the new speed (s+40), the new time would be t-12/60 hours. The distance is the same

(s+40)(t - 1/5) = 145
(s+40)(145/s - 1/5) = 145

Putting it all over 5s, we get for the numerator:

(s+40)(725-s) = 725s
725s + 29000 - s^2 - 40s - 725s = 0

(We can disregard the denominator of 5s, since it is not zero here, and the fraction is zero when the numerator is zero)

s^2 + 40s - 29000 = 0
s = 151.46 mi/hr

The new required speed is s+40 = 191.46 mi/hr

Answer 2

how did s^2 + 40s - 29000 = 0
become s = 151.46 mi/hr?