SOLUTION: When Ace Airlines changed to planes that flew 100 km/h faster than its old one the time of its 2800 km Dallas-Seattle flight was reduced by 30 min. Find the speed of the new plane

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Question 167947This question is from textbook
: When Ace Airlines changed to planes that flew 100 km/h faster than its old one the time of its 2800 km Dallas-Seattle flight was reduced by 30 min. Find the speed of the new planes. This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r= the speed of the old planes Dallas-Seattle in km/hr
Let t= the old plane's time Dallas-Seattle in hrs
Given is
d+=+2800km
2800+=+r%2At
t+=+2800%2Fr
Also given is
2800+=+%28r+%2B+100%29%2A%28t+-+.5%29
2800+=+%28r+%2B+100%29%2A%282800%2Fr+-+.5%29
2800+=+2800+%2B+280000%2Fr+-+.5r+-+50
Subtract 2800 from both sides
0+=+280000%2Fr+-+.5r+-+50
Multiply both sides by r
280000+-+.5r%5E2+-+50r+=+0
Divide both sides by .5
-r%5E2+-+100r+%2B+560000+=+0
Using the quadratic formula
r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

r+=+%28100+%2B-+sqrt%28+10000+%2B+2240000+%29%29%2F-2%29+
r+=+%28100+%2B-+sqrt%28+2250000+%29%29%2F-2%29+
r+=+%28100+%2B+1500%29+%2F+-2 reject this since it is negative
r+=+%28100+-+1500%29+%2F+-2
r+=+-1400+%2F+-2
r+=+700
The speed of the new planes is r+%2B+100+=+800 km/hr
check answer:
t+=+2800%2Fr
t+=+2800%2F700
t+=+4hrs
2800+=+%28r+%2B+100%29%2A%28t+-+.5%29
2800+=+%28700+%2B+100%29%2A%284+-+.5%29
2800+=+800%2A3.5
2800+=+2800
OK