SOLUTION: In a certain number of hours a woman traveled 5 km. If she had traveled 2 km more per hour, it would have taken her 3 h less to make the journey. How many kilometers did she travel

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: In a certain number of hours a woman traveled 5 km. If she had traveled 2 km more per hour, it would have taken her 3 h less to make the journey. How many kilometers did she travel      Log On


   

Question 1105126: In a certain number of hours a woman traveled 5 km. If she had traveled 2 km more per hour, it would have taken her 3 h less to make the journey. How many kilometers did she travel per hour? (Keep three significant digits.)
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her normal speed in km/hr
Let +t+ = her normal time in hrs
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(1) +5+=+s%2At+
(2) +5+=+%28+s%2B2+%29%2A%28+t+-+3+%29+
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(2) +5+=+s%2At+%2B+2t+-+3s+-+6+
(2) +s%2At+%2B+2t+-+3s+=+11+
(2) +s%2A%28+t+-+3+%29+%2B+2t+=+11+
and
(1) +s+=+5%2Ft+
(2) +%285%2Ft%29%2A%28+t+-+3+%29+%2B+2t+=+11+
(2) +5%2A%28+t+-+3+%29+%2B+2t%5E2+=+11t+
(2) +5t+-+15+%2B+2t%5E2+-+11t+=+0+
(2) +2t%5E2+-+6t+-+15+=+0+
use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+-6+
+c+=+-15+
+t+=+%28+-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A2%2A%28-15%29+%29%29%2F%282%2A2%29+
+t+=+%28+6+%2B-sqrt%28+36+%2B+120+%29%29+%2F+4+
+t+=+%28+6+%2B+sqrt%28+156+%29+%29%2F4+
+t+=+%28+6+%2B+12.49+%29%2F4+
+t+=+18.49%2F4+
+t+=+4.6225+
and
(1) +s+=+5%2Ft+
(1) +s+=+5%2F4.6225+
(1) +s+=+1.0817+
She normally traveled 1.0817 km/hr
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check:
(2) +5+=+%28+s%2B2+%29%2A%28+t+-+3+%29+
(2) +5+=+%28+1.0817%2B2+%29%2A%28+4.6225+-+3+%29+
(2) +5+=+3.0817%2A1.6225+
(2) +5+=+5.00006+
close enough!
check the math and get another
opinion if needed

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your "time" equation is

5%2Fx - 5%2F%28x%2B2%29 = 3    hours,


where x i the woman's normal rate of walking, in km/h.


Solve for x.


5*(x+2) - 5x = 3x*(x+2)

5x + 10 - 5x = 3x^2 + 6x,

3x^2 + 6x - 10 = 0  ====>

x%5B1%2C2%5D = %28-6+%2B-+sqrt%286%5E2+%2B+4%2A3%2A10%29%29%2F%282%2A3%29 = %28-6+%2B-+sqrt%28156%29%29%2F6.


Only positive root makes sense  x%5B1%5D = %28-6+%2B+sqrt%28156%29%29%2F6 = 1.0817 km/h.

Solved.