SOLUTION: two hikers, Arione and Jairus, started from the same place at the same time and walked towards Lipa City, which is 90 kilometers away from their place. Arione walked 1 kilometer

Algebra ->  Test -> SOLUTION: two hikers, Arione and Jairus, started from the same place at the same time and walked towards Lipa City, which is 90 kilometers away from their place. Arione walked 1 kilometer      Log On


   

Question 979823: two hikers, Arione and Jairus, started from the same place
at the same time and walked towards Lipa City, which is 90
kilometers away from their place. Arione walked 1
kilometer per hour faster than Jairus and reached Lipa 1
hour before him. Find the rate of each hiker.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Jairus's speed in km/hr
+s+%2B+1+ = Arione's speed in km/hr
Let +t+%2B+1+ = Jairus's time in hrs
+t+ = Arione's time in hrs
---------------------------------
Jairus's equation:
(1) +90+=+s%2A%28+t%2B1+%29+
Arione's equation:
(2) +90+=+%28+s%2B1+%29%2At+
---------------------
(2) +s%2At+%2B+t+=+90+
and
(1) +s+=+90%2F%28+t+%2B+1+%29+
Substitute (1) into (2)
(2) +%28+90%2F%28+t%2B1+%29+%29%2At+%2B+t+=+90+
Multiply both sides by +t%2B1+
(2) +90t+%2B+t%2A%28+t%2B1+%29+=+90%2A%28+t%2B1+%29+
(2) +90t+%2B+t%5E2+%2B+t+=+90t+%2B+90+
(2) +t%5E2+%2B+t+-+90+=+0+
I notice that +90+=+9%2A10+, so
(2) +%28+t+%2B+10+%29%2A%28+t+-+9+%29+=+0+
+t+=+9+ ( time must be positive )
and
(1) +90+=+s%2A%28+t%2B1+%29+
(1) +90+=+s%2A%28+9%2B1+%29+
(1) +90+=+10s+
(1) +s+=+9+
and
+s%2B1+=+10+
Ariones's rate is 10 km/hr
Jairus's rate is 9 km/hr
-----------------------
check:
(2) +90+=+%28+s%2B1+%29%2At+
(2) +90+=+%28+9%2B1+%29%2A9+
(2) +90+=+90+
and
(1) +90+=+s%2A%28+t%2B1+%29+
(1) +90+=+9%2A%28+9%2B1+%29+
(1) +90+=+90+
OK