SOLUTION: A person has 6 hours at his disposal. How far may he ride into the country at 8 miles an hour, that he may return home in time, walking back at the rate of 4 miles per hour?

Algebra ->  Equations -> SOLUTION: A person has 6 hours at his disposal. How far may he ride into the country at 8 miles an hour, that he may return home in time, walking back at the rate of 4 miles per hour?       Log On


   

Question 726372: A person has 6 hours at his disposal. How far may he ride into the country at 8 miles an hour, that he may return home in time, walking back at the rate of 4 miles per hour?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance he rides in
Let +t+ = time in hrs to ride in
given:
(1) +d+=+8t+
(2) +d+=+4%2A%28+6+-+t+%29+
-------------------
Substitute (1) into (2)
(2) +8t+=+4%2A%28+6+-+t+%29+
(2) +8t+=+24+-+4t+
(2) +12t+=+24+
(2) +t+=+2+
and, since
(1) +d+=+8%2A2+
(1) +d+=+16+
He can ride 16 miles into country
check:
(2) +d+=+4%2A%28+6+-+t+%29+
(2) +16+=+4%2A%28+6+-+2+%29+
(2) +16+=+4%2A4+
(2) +16+=+16+
OK