Problema Solution
Madi finished a triathlon involving swimming, bicycling, and running. Madi's bicycling speed was about 6 times her swimming speed, and her running speed was about 5 miles per hour greater than her swimming speed.
a. Determine expressions for the seperate time of her events if she swam .5 miles, bicycled 25 miles, and ran 6 miles.
b. If she finished the triathlon in 2.5 hours, write an equation to express the situation
c. Solve the expression to find Madi's swimming, bicycling, and running rates.
Answer provided by our tutors
'b' for biking speed
'r' for running speed
's' for swimming speed
b = 6s
r=s+5
a: .5/s + 25/b + 6/r
b: 25 = .5/s + 25/b + 6/r
c:
substituting for 'b' and 'r':
2.5 = .5/s + 25/(6s) + 6/(s+5)
gives this quadratic equation:
7.5s^2 + 5.5s - 70 = 0
yields a positive value of s=2.71
b= 2.71 * 6 = 16.26
r = 2.71 + 5 = 7.71
so her swimming speed was close to 3, her biking speed was just over 16 and her running speed was close to 8