SOLUTION: On a 42km go-kart course, Arshia drives 0.4km/hr faster than Sarah, but has engine trouble and stops for 30min. Arshia arrives at the finish line 15min after Sarah. How fast did ea

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: On a 42km go-kart course, Arshia drives 0.4km/hr faster than Sarah, but has engine trouble and stops for 30min. Arshia arrives at the finish line 15min after Sarah. How fast did ea      Log On

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 Question 519177: On a 42km go-kart course, Arshia drives 0.4km/hr faster than Sarah, but has engine trouble and stops for 30min. Arshia arrives at the finish line 15min after Sarah. How fast did each girl drive and how long did each girl take to finish the course?Answer by ankor@dixie-net.com(15661)   (Show Source): You can put this solution on YOUR website!On a 42km go-kart course, A drives 0.4km/hr faster than S, but has engine trouble and stops for 30min. A arrives at the finish line 15min after S. How fast did each drive and how long did each take to finish the course? : Let s = S's speed then (s+.4) = A's speed : Change 30 min to .5 hrs Change 15 min to .25 hrs : Write a time equation, time = dist/speed : A's time = S's time + .25 hr + .5 = + .25 = + .25 -.5 = - .25 : multiply by s(s+.4), results: 42s = 42(s+.4) - .25s(s+.4) 42s = 42s + 16.8 - .25s^2 - .1s : Combine like terms on the left .25s^2 + .1s + 42s - 42s - 16.8 = 0 .25s^2 + .1s - 16.8 = 0 ; Get rid of those decimals, multiply by 100 25s^2 + 10s - 1680 = 0 : simplify, divide by 5 5s^2 + 2s - 336 = 0 : you can use the quadratic formula to solve, but this will factor to: (5s+42)(s-8) = 0 : Positive solution is what we want here s = 8 km/hr is S's speed then, obviously, 8.4 km/h is A's speed : : : See if that work out + .5 = + .25 5 + .5 = 5.25 + .25 5.5 = 5.5; confirms our solutions