SOLUTION: Two planes make a 1000 mile flight, one flying 75 mph faster than the other. the quicker plane makes the trip 3 hours faster. How long did it take the slower plane to complete th

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Question 657891: Two planes make a 1000 mile flight, one flying 75 mph faster than the other. the quicker plane makes the trip 3 hours faster. How long did it take the slower plane to complete the flight?
Hi! I've tried this problem several ways and nothing is working out for me. Can you show me a solution please? Thank you!
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Let s be the speed of the slower plane and s+75 be the speed of the faster plane.
The time it takes the slower plane to make the flight is 1000%2Fs
The time it takes the faster plane to make the flight is 1000%2F%28s%2B75%29
The difference in these two times is 3 hours, so
1000%2Fs+-+1000%2F%28s%2B75%29+=+3

%281000%2As%2B75000%29%2F%28s%5E2%2B75%2As%29+-+%281000%2As%29%2F%28s%5E2%2B75%2As%29+=+3
%281000%2As+%2B+75000+-+1000%2As%29%2F%28s%5E2+%2B+75%2As%29+=+3
75000%2F%28s%5E2+%2B+75%2As%29+=+3
%28s%5E2+%2B+75%2As%29%2A%2875000%2F%28s%5E2+%2B+75%2As%29%29+=+%28s%5E2+%2B+75%2As%29%2A3
75000+=+3%2As%5E2+%2B+225%2As
25000+=+s%5E2+%2B+75%2As
s%5E2+%2B+75s+-+25000+=+0
We can solve for s using the quadratic equation s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ with a=1, b=75, and c=-25000
s+=+%28-75+%2B-+sqrt%28+75%5E2-4%2A1%2A%28-25000%29+%29%29%2F%282%2A1%29+
s+=+%28-75+%2B-+sqrt%28+5625%2B100000+%29%29%2F2+
s+=+%28-75+%2B-+sqrt%28+105625+%29%29%2F2+
s+=+%28-75+%2B-+325%29%2F2+
So s = -200 or s = 125. We'll ignore the negative answer because the planes are not flying backward.
So the slower plane is flying at 125 mph and completes the trip in 8 hours.
The faster plane is flying at 200 mph and completes the trip in 5 hours.