Write the solution as a mixed number or a fraction in lowest terms.

Question

A runner has a track lap time of 1 minute while at a run, 4 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/3 at a jog, and 4/15 at a walk, what is the total track lap time of the runner? Write the solution as a mixed number or a fraction in lowest terms.

Answer 1

This is a D-I-R-T (Distance Is Rate times Time) problem.        D = R*T

So,     T = D/R

" a track lap time of 1 minute while at a run"    means  running rate is   (1 lap)/(1 minute)
"4 minutes while at a jog"     means   jogging rate is (1 lap)/(4 minutes)
"7 minutes while at a walk"    means   walking rate is (1 lap)/(7 minutes)

The distances are also given --
      (2/5 lap) while running
      (1/3 lap) while jogging
      (4/15 lap( while walking
                           [note:  good to check that (2/5 lap)+(1/3 lap)+4/15 lap) = (1 lap)]
                             6/15 + 5/15 + 4/15 = 15/15 = 1

"what is the total track lap time of the runner?"

Total time     =             time running                +              time jogging                 +     time walking
                   =   (2/5 lap) / ( (1 lap)/(1 min) )  +  (1/3 lap) / ( (1 lap)/(4 min) )     +   (4/15 lap) / ( (1 lap)/(7 min) )
     NOTE:  To divide by fraction, invert denominator and multiply.   Lap cancels out.
                   =            (2/5) min                     +       (4/3) min                             +     (48/15) min
                   =            6/15 min                      +        20/15 min                          + 48/15 min         
        NOTE:  Least Common Denominator (LCD) is 15
                   =    74/15 min
                   =  4  14/15 min        (also 4 minutes and 56 seconds)