SOLUTION: Felipe jogs for 9 miles and then walks another 9 miles. He jogs 4.5 miles per hour faster than he walks, and the entire distance of 18 miles takes 3 hours. Find the rate at which

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Felipe jogs for 9 miles and then walks another 9 miles. He jogs 4.5 miles per hour faster than he walks, and the entire distance of 18 miles takes 3 hours. Find the rate at which      Log On

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Question 662292: Felipe jogs for 9 miles and then walks another 9 miles. He jogs 4.5
miles per hour faster than he walks, and the entire distance of 18 miles takes 3 hours. Find the rate at which he walks and the rate at which he jogs.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = his time spent jogging in hrs
+3+-+t+ = his time spent walking in hrs
Let +w+ = his speed walking in mi/hr
+w+%2B+4.5+ = his speed jogging
----------
Equation for jogging:
(1) +9+=+%28+w+%2B+4.5+%29%2At+
Equation for walking:
(2) +9+=+w%2A%28+3+-+t+%29+
--------------------
(2) +9+=+3w+-+w%2At+
(2) +w%2At+=+3w+-+9+
(2) +t+=+3+-+9%2Fw+
Substitute (2) into (1)
(1) +9+=+%28+w+%2B+4.5+%29%2A%28+3+-+9%2Fw+%29++
(1) +9+=+3w+%2B+13.5+-+9+-+40.5%2Fw+
(1) +18+-+13.5+=+3w+-+40.5%2Fw+
(1) +4.5+=+3w+-+40.5%2Fw+
(1) +4.5w+=+3w%5E2+-+40.5+
(1) +3w%5E2+-+4.5w+-+40.5+=+0+
(1) +2w%5E2+-+3w+-+27+=+0+
use quadratic formula
+w+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A%28-27%29+%29%29++%2F+%282%2A2%29+
+w+=+%28+3+%2B-+sqrt%28+9+%2B+216+%29%29++%2F+4+
+w+=+%28+3+%2B-+sqrt%28+225+%29%29++%2F+4+
+w+=+%28+3+%2B+15%29++%2F+4+
+w+=+18%2F4+
+w+=+4.5+ ( ignore negative root )
+w+%2B+4.5+=+9+
he walks 4.5 mi/hr and jogs 9 mi/hr
check:
(2) +9+=+4.5%2A%28+3+-+t+%29+
(2) +9+=+13.5+-+4.5t+
(2) +4.5t+=+13.5+-+9+
(2) +4.5t+=+4.5+
+t+=+1+
and
(1) +9+=+%28+4.5+%2B+4.5+%29%2At+
(1) +9+=+9t+
+t+=+1+
OK