SOLUTION: Bret started on a 80-mile bicycle ride at 15 miles per hour. After a time he became a little tired and slowed down to 10 miles per hour for the rest of the trip. The entire trip of

Algebra ->  Finance -> SOLUTION: Bret started on a 80-mile bicycle ride at 15 miles per hour. After a time he became a little tired and slowed down to 10 miles per hour for the rest of the trip. The entire trip of      Log On


   



Question 885668: Bret started on a 80-mile bicycle ride at 15 miles per hour. After a time he became a little tired and slowed down to 10 miles per hour for the rest of the trip. The entire trip of 80 miles took
5 1/2 hours. How far had Bret ridden when he reduced his speed to 10 miles per hour?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance Bret had traveled
at +15+ mi/hr
Let +t+ = time spent traveling at
+15+ mi/hr
+80+-+d+ = distance Bret traveled at
+10+ mi/hr
+5.5+-+t+ = time spent traveling at
+10+ mi/hr
----------------
Equation for riding at 15 mi/hr:
(1) +d+=+15t+
Equation for riding at 10 mi/hr
(2) +80+-+d+=+10%2A%28+5.5+-+t+%29+
(2) +80+-+d+=+55+-+10t+
(2) +d+-+10t+=+25+
---------------------
Substitute (1) into (2)
(2) +d+-+10t+=+25+
(2) +15t+-+10t+=+25+
(2) +5t+=+25+
(2) +t+=+5+
(1) +d+=+15t+
(1) +d+=+15%2A5+
(1) +d+=+75+
----------------
Bret had ridden 75 mi at 15 mi/hr
check:
+80+-+d+=+80+-+75+
+80+-+d+=+5+
----------------
(2) +80+-+75+=+10%2A%28+5.5+-+5+%29+
(2) +5+=+10%2A.5+
(2) +5+=+5+
OK