SOLUTION: A race consists of a 20-mile bike ride and a 12-mile run. Jen’s rate while biking is 4 mi/h faster than while running. She completes the race in 4 hours. a. Let r be Jen’s rate

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A race consists of a 20-mile bike ride and a 12-mile run. Jen’s rate while biking is 4 mi/h faster than while running. She completes the race in 4 hours. a. Let r be Jen’s rate      Log On

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Question 733167: A race consists of a 20-mile bike ride and a 12-mile run. Jen’s rate while
biking is 4 mi/h faster than while running. She completes the race in 4 hours.
a. Let r be Jen’s rate while biking.
Copy and complete the table.
b. Use the information in the Time
column to write a rational equation.
c. Solve the equation to find Jen’s rate
while biking.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
rates:
biking: +r+ mi/hr
running: +r+-+4+ mi/hr
-------------
distances:
biking: +20+ mi
running: +12+ mi
-------------
times:
biking: +20%2Fr+ hrs
running: +12%2F%28+r+-+4+%29+
--------------
+20%2Fr+%2B+12%2F%28r+-+4%29+=+4+
Multiply both sides by +r%2A%28+r+-+4+%29+
+20%2A%28+r+-+4+%29+%2B+12r+=+4r%2A%28+r+-+4+%29+
+20r+-+80+%2B+12r+=+4r%5E2+-+16r+
+4r%5E2+-+20r+-+16r+-+12r+%2B+80+=+0+
+4r%5E2+-+48r+%2B+80+=+0+
+r%5E2+-+12r+%2B+20+=+0+
+%28+r+-+2+%29%2A%28+r+-+10+%29+=+0+
The 2 answers are:
+r+=+2+
+r+=+10+
+r+ can't be +2+ since I have to subtract +4+ from it
to get the running speed, so
Jen's rate while biking is 10 mi/hr
check:
+20%2A%28+r+-+4+%29+%2B+12r+=+4r%2A%28+r+-+4+%29+
+20%2A%28+10+-+4+%29+%2B+12%2A10+=+4%2A10%2A%28+10+-+4+%29+
+20%2A6+%2B+120+=+40%2A6+
+240+=+240+
OK