SOLUTION: Jim Williamson began a 96-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole t

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Question 640952: Jim Williamson began a 96-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 4 miles per hour and rides at 20 miles per hour, find the amount of time he spent on the bicycle.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hours he spent walking
+6+-+t+ = time in hours he spent on bike
Let +d+ = distance Jim walked in miles
+96+-+d+ = distance in miles he biked
Equation for walking:
(1) +d+=+4t+
Equation for biking:
(2) +96+-+d+=+20%2A%28+6-t+%29+
---------------------
Substitute (1) into (2)
(2) +96+-+4t+=+120+-+20t+
(2) +20t+-+4t+=+120+-+96+
(2) +16t+=+24+
(2) +t+=+3%2F2+
+6+-+t+=+6+-+3%2F2+
+6+-+t+=+9%2F2+
Jim's time spent on bike is 4 and a half hours
check:
(1) +d+=+4%2A%283%2F2%29+
(1) +d+=+6+
and
(2) +96+-+d+=+20%2A%28+6-%283%2F2%29+%29+
(2) +-d+=+20%2A%289%2F2%29+-+96+
(2) +-d+=+90+-+96+
(2) +-d+=+-6+
(2) +d+=+6+
OK