Andrew M. answered • 04/06/17

Tutor

New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

We have a time in minutes and a rate in km/hr.

We need to get our units the same...

5 km in 20 mins = 5 km in 1/3 hour

If we run 4 km at a rate of r and a time t hour

We run 1 km at a rate of (r+2) and a time (1/3 - t) hours

Distance = rate*time is our basic formula.. d=rt

4 = rt {equation 1: first 4 km}

1 = (r+2)(1/3-t) {equation 2: last km}

Working on equation 2:

1 = r/3 - rt + 2/3 - 2t

3 = r - 3rt + 2 - 6t

r - 3rt - 6t = 1

We have 2 equations ...

rt = 4 {equation 1}

r - 3rt - 6t = 1 {equation 2}

Replace rt with 4 in equation 2

r - 3(4) - 6t = 1

r - 12 - 6t = 1

r - 6t = 13

From rt=4 we can say t = 4/r

r - 6(4/r) = 13

r - 24/r = 13

multiply through by r

r

^{2}- 24 = 13rr

^{2}- 13r - 24 = 0from quadratic equation

r = [13 ±√((-13)

^{2}-4(1)(-24))]/2(1)r = (13 ±√265)/2

r = 14.64 km/hr

r+2 = 16.64 km/hr for last km of the race