SOLUTION: A person walks to the top of a mountain at a rate of 4mi/hr and down the mountain the same way at a rate of 3 mi/hr. If she walks up and down in 2 hours, how far (mi) is it to the

Question 950063: A person walks to the top of a mountain at a rate of 4mi/hr and down the mountain the same way at a rate of 3 mi/hr. If she walks up and down in 2 hours, how far (mi) is it to the top?

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
d=distance to top; r1= rate up; r2=rate down; T=total time
T=(d/r1)+(d/r2)
2 hrs=d((1/r1)+(1/r2))
2 hrs=d(1/4mph+1/3mph)
2 hrs=d(3/12mph+4/12mph)
2 hrs=d(7/12mph) Multiply each side by (12/7 mph)
24/7 mi=d ANSWER: It is 3 and 3/7 miles to the top.
CHECK
2 hrs=(24/7 mi/4 mph)+ (24/7 mi/3mph)
2 hrs=(6/7 hrs)+(8/7 hrs)
2 hrs=(14/7 hrs)
2 hrs=2 hrs

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