SOLUTION: A girl lives 6 miles from school. On her way home, she skates 4 miles before a wheel falls off her skates. It then takes her the same amount of time to walk the rest of the way hom

Question 733501: A girl lives 6 miles from school. On her way home, she skates 4 miles before a wheel falls off her skates. It then takes her the same amount of time to walk the rest of the way home as it took her to skate the first 4 miles. She can skate 3mph faster than she walks. How fast can she skate?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
to solve this problem recognize that this is a rate problem with the following equation
rate times time = distance
let t be the time it takes her to skate 4 miles and also the time it takes her to walk 2 miles, also let r+3 be her skating rate and r be her walking rate
so here we have
(r+3)t + rt = 6 and
(r+3)t = 4 and rt = 2
expand the first equation and we get
rt + 3t + rt = 6
substitute 2 for rt and we have
2 + 3t + 2 = 6 and 3t = 2 with t = 2/3
her walking rate is r times 2/3 = 2 or r = 3 mph and her skating rate is 3 + 3 or 6 mph

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