SOLUTION: A motorist drove 120 miles before running out of gas and walking 4 miles to a gas station. The rate of the motorist in the car was ten times the rate walking. The time spent walkin

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A motorist drove 120 miles before running out of gas and walking 4 miles to a gas station. The rate of the motorist in the car was ten times the rate walking. The time spent walkin      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1086524: A motorist drove 120 miles before running out of gas and walking 4 miles to a gas station. The rate of the motorist in the car was ten times the rate walking. The time spent walking was 2 hours less than the time spent driving. How long did it take for the motorist to drive the 120 miles?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = the rate walking in mi/hr
+10r+ = the rate driving the car
Let +t+ = the time in hrs spent driving
+t+-+2+ = the time in hrs spent walking
----------------------------------------
Equation for walking:
(1) +4+=+r%2A%28+t+-+2+%29++
Equation for driving:
(2) +120+=+10r%2At+
----------------------
(2) +r+=+12%2Ft+
Plug (2) into (1)
(1) +4+=+%28+12%2Ft+%29%2A%28+t-2+%29+
(1) +4t+=+12%2A%28+t-2+%29+
(1) +4t+=+12t+-+24+
(1) +8t+=+24+
(1) +t+=+3+ hrs
--------------------------
The motorist took 3 hrs to drive the 120 mi
--------------------------
check:
(2) +120+=+10r%2At+
(2) +120+=+10r%2A3+
(2) +3r+=+12+
(2) +r+=+4+ mi/hr
and
(1) +4+=+r%2A%28+t+-+2+%29++
(1) +4+=+r%2A%28+3+-+2+%29++
(1) +r+=+4+ mi/hr
OK