SOLUTION: a motorcycle breaks down and the rider has to walk the rest of the way to work.the motorcycle was traveling at 45mi/h,and the rider walks at a speed of 6mi/h.the distance from home

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a motorcycle breaks down and the rider has to walk the rest of the way to work.the motorcycle was traveling at 45mi/h,and the rider walks at a speed of 6mi/h.the distance from home      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 118934: a motorcycle breaks down and the rider has to walk the rest of the way to work.the motorcycle was traveling at 45mi/h,and the rider walks at a speed of 6mi/h.the distance from home to work is 25 miles,and the total time for the trip was 2 hrs.how far did the motorcycle go before it broke down?
Answer by mayank(15) About Me  (Show Source):
You can put this solution on YOUR website!
Let the motorcycle ride for x hrs and the rider walk for y hrs.
Then as we know total distance travelled is 25 miles and rider is traveling at 6 mi/hr and motorcycle at 45mil/hr we can have equation as
45x+6y=25----(i)
now as total duration of trip is 2 hrs, x+y=2---(ii)
Thus we get two equations and we need to find two variables.
multiplying equation (ii) by 6 we get 6x+6y=12---(iii)
subtracting equation iii from equation (i) we get 39x=13 or x=1/3
Substituting value of x in equation (ii) we get y=5/3.
Thus total miles covered by motorcycle is 45x= 45*(1/3)=45/3=15 miles.
Thus ans is 15 miles.