SOLUTION: a motorist drove 72 miles before running out of gas, and then walking 4 miles to the gas station. The driving rate of the motorist was 12 times his walking rate. THe time spent dri

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a motorist drove 72 miles before running out of gas, and then walking 4 miles to the gas station. The driving rate of the motorist was 12 times his walking rate. THe time spent dri      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 942715: a motorist drove 72 miles before running out of gas, and then walking 4 miles to the gas station. The driving rate of the motorist was 12 times his walking rate. THe time spent drivin and walking was 3.5 hours. Find the rate at which the motorist walks.
thank u!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time spent driving in hrs
+3.5+-+t+ = time spent walking in hrs
Let +r+ = his rate walking in mi/hr
+12r+ = his rate driving in mi/hr
--------------------------------
Equation for driving:
(1) +72+=+12r%2At+
Equation for walking:
(2) +4+=+r%2A%28+3.5+-+t+%29+
---------------------
(1) +r+=+6%2Ft+
Substitute (1) into (2)
(2) +4+=+%28+6%2Ft+%29%2A%28+3.5+-+t+%29+
(2) +4+=+21%2Ft+-+6+
(2) +4t+=+21+-+6t+
(2) +10t+=+21+
(2) +t+=+2.1+
------------------
(1) +72+=+12r%2A2.1+
(1) +72+=+25.2r+
(1) +r+=+2.857+ mi/hr
The motorist walks at 2.857 mi/hr
check:
(2) +4+=+r%2A%28+3.5+-+t+%29+
(2) +4+=+2.857%2A%28+3.5+-+2.1+%29+
(2) +4+=+2.857%2A1.4+
(2) +4+=+4+
OK