SOLUTION: Nickola swam at a rate of 3 ​km/hr and ran at a rate of 15 ​km/hr for a total distance traveled of 73.5 km. If he completed the race in 6.5 ​hours, how long

Algebra ->  Finance -> SOLUTION: Nickola swam at a rate of 3 ​km/hr and ran at a rate of 15 ​km/hr for a total distance traveled of 73.5 km. If he completed the race in 6.5 ​hours, how long      Log On


   

Question 1086593: Nickola swam at a rate of 3 ​km/hr and ran at a rate of 15 ​km/hr for a total distance traveled of 73.5 km. If he completed the race in 6.5 ​hours, how long did he take to complete each part of the​ race?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs to complete the
swimming part of the race
+6.5+-+t+ = time in hrs to complete the
running part
Let +d+ = distance in km that he swam
+73.5+-+d+ = distance in km that he ran
---------------------------------------
Equation for the swimming part:
(1) +d+=+3t+
Equation for the running part:
(2) +73.5+-+d+=+15%2A%28+6.5+-+t+%29+
---------------------------------------
Plug (1) into (2)
(2) +73.5+-+3t+=+15%2A%28+6.5+-+t+%29+
(2) +73.5+-+3t+=+97.5+-+15t+
(2) +12t+=+24+
(2) +t+=+2+
and
+6.5+-+t+=+6.5+-+2+
+6.5+-+t+=+4.5+
-----------------------
He took 2 hrs to finish the swimming part
He took 4.5 hrs to finish the running part
-----------------------
check:
(1) +d+=+3t+
(1) +d+=+3%2A2+
(1) +d+=+6+ km
and
(2) +73.5+-+d+=+15%2A%28+6.5+-+t+%29+
(2) +73.5+-+d+=+15%2A%28+6.5+-+2+%29+
(2) +73.5+-+d+=+15%2A4.5+
(2) +73.5+-+d+=+67.5+
(2) +d+=+6+
OK