Answer:
Step-by-step explanation:
<u>Equation</u>
Let s represent the speed of the faster plane. Then its travel time is ...
time = distance/speed = 3600/s
travel time for the slower plane is ...
time = distance/speed = 3600/(s -200)
The difference in these times is 1.5 hours, so we have ...
3600/(s -200) -3600/s = 1.5
<u>Solution</u>
Multiplying by (2/3)s(s -200), we get ...
2400(s) -2400(s -200) = s(s -200)
s^2 -200s -480000 = 0 . . . . . . . . . . rewrite in standard form
(s -800)(s +600) = 0 . . . . . . . . . . . . . factor
The positive value of s that makes a factor zero is s = 800.
<u>Conclusion</u>
The speed of the faster plane was 800 km/h; of the slower plane, 600 km/h.
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<em>Check</em>
The travel time for the faster plane was 3600/800 = 4.5 hours. For the slower plane, 3600/600 = 6 hours, a difference of 1.5 hours.
