SOLUTION: A turbo-jet flies 50 mph. faster than a super-prop plane. If a turbo-jet goes 2000 miles in 3 hours less time than it takes the super-prop to go 2800 miles, find the speed of each

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Question 409828: A turbo-jet flies 50 mph. faster than a super-prop plane. If a turbo-jet goes 2000 miles in 3 hours less time than it takes the super-prop to go 2800 miles, find the speed of each plane.
I set this up as 2800/10 + 50 = 2000/t-3
when I factor the GCF of t(t-3) I cannot get any further...please help!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
s = speed of super-prop
j = speed of turbo-jet
t = time for super-prop to go 2800 mi
given:
(1) j+=+s+%2B+50
(2) 2000+=+j%2A%28t+-+3%29
(3) 2800+=+s%2At
This is 3 equations and 3 unknowns, so it's solvable
Substitute (1) in (2)
(2) 2000+=+%28s+%2B+50%29%2A%28t+-+3%29
(2) 2000+=+s%2At+%2B+50t++-+3s+-+150
Substitute (3) in (2)
(2) 2000+=+2800+%2B+50%2A%282800%2Fs%29+-+3s+-+150
(2) 3s+=+2800+-+2000+-+150+%2B+50%2A%282800%2Fs%29
(2) 3s+=+650+%2B+50%2A%282800%2Fs%29
(2) 3s%5E2+=+650s+%2B+140000
(2) 3s%5E2+-+650s+-+140000=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+3
b+=+-650

s+=+%28+650+%2B-+sqrt%28++422500+%2B+1680000+%29%29%2F+6+
s+=+%28+650+%2B-+sqrt%28++2102500+%29%29%2F+6+
s+=+%28+650+%2B-+1450%29%2F+6+
s+=+2100%2F6
s+=+350
and, since
(1) j+=+s+%2B+50
(1) j+=+400
The turbo-jet has a speed of 400 mi/hr
The super-prop has a speed of 350 mi/hr
check answer:
(2) 2000+=+%28s+%2B+50%29%2A%28t+-+3%29
(2) 2000+=+%28350+%2B+50%29%2A%28t+-+3%29
(2) 2000%2F400+=+t+-+3
(2) t+=+5+%2B+3
(2) t+=+8 hrs
and
(3) 2800+=+s%2At
(3) 2800+=+350%2A8
(3) 2800+=+2800
OK