Math question, please help

Question

A runner has a track lap time of 1 minute while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 1/6 of the lap is paced at a run, 1/4 at a jog, and 7/12 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

rate x time = distance

We are looking for time, so we solve for it, dividing both side of the above equation by rate to get time.

time = distance / rate

The runner's rates are:

running: 1 track/minute (completes the track in a minute)

jogging: 1/5 track/minute (think the runner completes the track in 5 minutes)

walking: 1/7 track/minute

So we need to add up the times the runner spent at each speed to get the total time.

time running = distance running/rate running = (1/6) / 1 = 1/6

time jogging = (1/4) / (1/5) here to divide fractions, we multiply by the reciprocal: (1/4) x (5/1) = 5/4

time walking = (7/12) / (1/7) = (7/12) x (7/1) = 49/12

We add the times: 1/6 + 5/4 + 49/12. Since we are adding we need a common denominator. Here it is 12.

For 1/6, multiply the numerator and denominator by 2 to get 2/12.

For 5/4, multiply the numerator and denominator by 3 to get 15/12.

Now add 2/12 + 15/12 + 49/12 = 66/12

Reduce by dividing the numerator and denominator by 6 to get 11/2.

Dividing 11 by 2 to get the mixed number, gives you 5 remainder 1. The 1 is put over the divisor (the bottom number) and the final answer is 5 1/2 minutes.