# SOLUTION: Two riders depart from city a to city b. One rider rides at 12 mph and other rider at 18 mph. Slower rider takes 1.5 hours longer to ride the distance. How long did it take both r

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: Two riders depart from city a to city b. One rider rides at 12 mph and other rider at 18 mph. Slower rider takes 1.5 hours longer to ride the distance. How long did it take both r      Log On

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 Click here to see ALL problems on Travel Word Problems Question 516178: Two riders depart from city a to city b. One rider rides at 12 mph and other rider at 18 mph. Slower rider takes 1.5 hours longer to ride the distance. How long did it take both riders to reach the destination How far is city a to city b? HELP!!!! How am I supposed to figure out how far the cities are from each other without any information on one or the other? And 1.5 hours to ride the distance??? AARRRGGGHHHH!!!!Found 2 solutions by scott8148, gc2000:Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!...calm...take deep breaths... d = r * t ___ they ride the same (equal) distance 18t = 12(t + 1.5) ___ 18t = 12t + 18 ___ 6t = 18 ___ t = 3 ___ t + 1.5 = 4.5 d = 18 * 3 = 54 Answer by gc2000(22)   (Show Source): You can put this solution on YOUR website!x = time for rider 1 to city b y = time for rider 2 to city b d = distance from a to city b d = (rate)*(time) what is known? two things: 1. distance is same for both riders 2. time for rider 2 is 1.5hrs longer, therefore the equation for this is: y = x + 1.5 therefore since distance is same: (rate rider1)*(time rider1) = (rate rider2)*(time rider2) (18mph)*(x hours) = (12mph)*(y hours) and substitute for y since y = x + 1.5: (18mph)*(x hours) = (12mph)*(x + 1.5 hours) 18x = 12(x + 1.5) 18x = 12x + 18 subtract 12x from both sides 6x = 18 divide both sides by 6 x = 3 time for rider1 is 3hrs. time for rider2 is 3 + 1.5 = 4.5 hours how far? d = (r)(t) d = (18)(3) = 54 distance = 54 miles check by d = (r)(t) for rider 2: d = (12)(4.5) d = 54, yes--answer checks out