SOLUTION: During the 1st part of a trip a man travels 100miles at a certain rate. On the 2nd part of the trip the man travels 14 miles at 5mph slower. What is the rate of speed during both p

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: During the 1st part of a trip a man travels 100miles at a certain rate. On the 2nd part of the trip the man travels 14 miles at 5mph slower. What is the rate of speed during both p      Log On


   

Question 319041: During the 1st part of a trip a man travels 100miles at a certain rate. On the 2nd part of the trip the man travels 14 miles at 5mph slower. What is the rate of speed during both parts of the trip. Whole trip takes 5hrs.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
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1.R%2AT1=100
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2.%28R-5%29%2AT2=14
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3.+T1%2BT2=5+
From eq. 1,
T1=100%2FR
From eq. 2,
T2=14%2F%28R-5%29
Substitute into eq. 3,
100%2FR%2B14%2F%28R-5%29=5
100%28R-5%29%2B14R=5R%28R-5%29
100R-500%2B14R=5R%5E2-25R
5R%5E2-25R=114R-500
5R%5E2-139R%2B500=0
Use the quadratic formula,
R+=+%28139+%2B-+sqrt%28+129%5E2-4%2A5%2A500+%29%29%2F%282%2A5%29+
R+=+%28139+%2B-+sqrt%289321%29%29%2F%2810%29+
Two solutions:
R=4.2 and R=23.6
R=4.2 can not work with this problem since R-5 would not make sense.
So then
highlight%28R+=+%28139+%2B+sqrt%289321%29%29%2F%2810%29%29+%29
and then,
highlight%28R-5+=+%2889+%2B+sqrt%289321%29%29%2F%2810%29%29+