SOLUTION: Plane A can travel 1500 miles in 1 hour less time than it takes plane B to travel 2500 miles. If the rate of plane B is 50 miles per hour greater than the rate of plane A. Find the

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Question 106884This question is from textbook
: Plane A can travel 1500 miles in 1 hour less time than it takes plane B to travel 2500 miles. If the rate of plane B is 50 miles per hour greater than the rate of plane A. Find the times and rates of both planes. This question is from textbook

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

distance(d) equals rate(r) times time(t) or d=rt; r=d/t and t=d/r
Let r=rate of Plane A
Then r+50=rate of Plane B
Time for Plane B to travel 2500 mi=2500/(r+50)
Time for Plane A to travel 1500 mi=1500/r
Now we are told that Plane A takes 1 hour less time than it takes Plane B, so:
(1500/r)+1=2500/(r+50) multiply each term by r(r+50) and we get:
1500(r+50)+r(r+50)=2500r get rid of parens (distributive law)
1500r+75000+r^2+50r=2500r subtract 2500r from both sides
1500r-2500r+75000+r^2+50r=2500r-2500r collect like terms
r^2-950r+75000=0 quadratic in standard form
Solve using the quadratic formula:
r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
r+=+%28950+%2B-+sqrt%28+950%5E2-4%2A1%2A75000+%29%29%2F%282%2A1%29+
r+=+%28950+%2B-+sqrt%28+902500-300000+%29%29%2F%282%29+
r+=+%28950+%2B-+sqrt%28602500+%29%29%2F%282%29+
r+=+%28950+%2B-+776.21+%29%29%2F%282%29+ So, looks like two solutions to me. Lets find out.
r+=+%28950%2B776.21+%29%29%2F%282%29+
r+=+%281726.21+%29%29%2F%282%29+
r+=+863.10+ mph-----------------------rate of plane A
Time for Plane A=1500/r=1500/863.10=1.738 hrs
r%2B50=863.10%2B50=913.10 mph---------------rate of Plane B
Time for Plane B=2500/913.10=2.738 hrs-------------------1 hr longer
and
x+=+%28950-776.21+%29%29%2F%282%29+
x+=+%28173.79+%29%29%2F%282%29+
x+=+86.895 mph----------------------rate of Plane A
Time for Plane A=1500/86.895=17.262 hrs
r%2B50=86.895%2B50=136.895 mph---------------rate of Plane B
Time for Plane B=2500/136.895=18.262 hrs-----------------------1 hr longer

Hope this helps-----ptaylor