SOLUTION: Carlos takes 3 hours longer than Ty to walk 30 miles; but if Carlos doubles his pace, he takes 2 hours less than Ty. Find (a) the rate at which Carlos walks and (b) the rate at whi

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Question 1116864: Carlos takes 3 hours longer than Ty to walk 30 miles; but if Carlos doubles his pace, he takes 2 hours less than Ty. Find (a) the rate at which Carlos walks and (b) the rate at which Ty walks.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Ty's time in hrs to walk +30+ mi.
when he walks at rate +r+ in mi/hr
+t+%2B+3+ = Carlos's time to do this
--------------------------------------------
Carlos's rate is +30%2F%28+t+%2B+3+%29+
Double this rate is +60%2F%28+t%2B3+%29+
Carlos's time at this rate is +t+-+2+
--------------------------------------------
Ty's equation:
+30+=+r%2At+
+r+=+30%2Ft+
Carlos's equation:
+30+=+%28+60%2F%28+t%2B3+%29+%29%2A%28+t+-+2+%29+
+30%2A%28+t%2B3+%29+=+60%2A%28+t+-+2+%29+
+t+%2B+3+=+2%2A%28+t+-+2+%29+
+t+%2B+3+=+2t+-+4+
+t+=+7+
--------------------
Ty's rate is:
+r+=+30%2Ft+
+r+=+30%2F7+ mi/hr
----------------------
Carlos's rate is:
+30%2F+%28+t+%2B+3+%29+=+30%2F%28+7+%2B+3+%29+
+30%2F10++=+3+ mi/hr
----------------------------------
check:
Double Carlos's pace is +6+ mi/hr
Two hrs less tiome than Ty is +7+-+2+=+5+ hrs
+30+=+6%2A5+
OK