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

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) (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:

So, looks like two solutions to me. Lets find out.

mph-----------------------rate of plane A
Time for Plane A=1500/r=1500/863.10=1.738 hrs
mph---------------rate of Plane B
Time for Plane B=2500/913.10=2.738 hrs-------------------1 hr longer
and

mph----------------------rate of Plane A
Time for Plane A=1500/86.895=17.262 hrs
mph---------------rate of Plane B
Time for Plane B=2500/136.895=18.262 hrs-----------------------1 hr longer

Hope this helps-----ptaylor

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