SOLUTION: Two track team members ran a 200-meter relay in 29 seconds. Each runner ran 100 meter. One runner ran 0.55 meters per second faster than the other. What was the speed of each runne

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Two track team members ran a 200-meter relay in 29 seconds. Each runner ran 100 meter. One runner ran 0.55 meters per second faster than the other. What was the speed of each runne      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 701652: Two track team members ran a 200-meter relay in 29 seconds. Each runner ran 100 meter. One runner ran 0.55 meters per second faster than the other. What was the speed of each runner?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in seconds for the faster runner
+29+-+t+ = the time in seconds for the slower runner
Let +s+ = the speed of the slower runner in m/sec
+s+%2B+.55+ = the speed of the faster runner in m/sec
--------------
For slower runner:
(1) +100+=+s%2A%28+29+-+t+%29+
For the faster runner:
(2) +100+=+%28+s+%2B+.55+%29%2At+
-----------------------
(1) +100+=+29s+-+s%2At+
and
(2) +t+=+100+%2F+%28+s+%2B+.55+%29+
Substitute (2) into (1)
(1) +100+=+29s+-+s%2A%28+100+%2F+%28+s+%2B+.55+%29%29+
(1) +100%2A%28+s+%2B+.55+%29+=+29s%2A%28+s+%2B+.55+%29+-+100s+
(1) +100s+%2B+55++=+29s%5E2+%2B+15.95s+-+100s+
(1) +29s%5E2++=+55+-+15.95s+
(1) +29s%5E2+%2B+15.95s+-+55+=+0+
use quadratic formula
+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+29+
+b+=+15.95+
+c+=+-55+
+s+=+%28+-15.95+%2B-+sqrt%28+15.95%5E2+-+4%2A29%2A%28-55%29+%29%29+%2F+%282%2A29%29+
+s+=+%28+-15.95+%2B-+sqrt%28+254.4025+%2B+6380+%29%29+%2F+58+
+s+=+%28+-15.95+%2B-+sqrt%28+6634.4+%29%29+%2F+58+
+s+=+%28+-15.95+%2B+81.452+%29+%2F+58+
+s+=+65.5+%2F+58+
+s+=+1.1293+
+s+%2B+.55+=+1.6793+
The slower runner's speed is 1.1293 m/sec
The faster runners speed is 1.6793 m/sec
---------
check:
(1) +100+=+1.1293%2A%28+29+-+t+%29+
(1) +100+=+32.7497+-+1.1293t+
(1) +1.1293t+=+67.2503+
(1) +t+=+59.5504+
------------------
(2) +100+=+%28+1.1293+%2B+.55+%29%2At+
(2) +100+=+1.6793%2At+
(2) +t+=+59.549+
close enough
hope I got it