SOLUTION: A cyclist traveled at a rate of 24mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby to

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A cyclist traveled at a rate of 24mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby to      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 118087: A cyclist traveled at a rate of 24mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Use d=rt where d is distance, r is the rate, and t is the time. Either direction the distance from home to the town is the same. Let's say that the time for the trip to town is t hours, then the time for the return trip is 4.9-t. So the distance to town is d=24t and the return trip distance is d=18%284.9-t%29. But these two distances are the same so we can say:

24t=18%284.9-t%29

24t=%2818%2A4.9%29-18t

24t%2B18t=18%2A4.9

42t=18%2A4.9

%286%2A7%29t=18%2A4.9

t=3%2A0.7=2.1. The trip to town took 2.1 hours, so the distance is d=24%2A2.1=50.4 miles.

Check:

The return trip must have taken 4.9-2.1=2.8 hours, so

18%2A2.8+=+50.4, and the answer checks.