On a certain trip, a motorist drove 6 miles at 20mph, 6 miles at 30mph, and 6 miles at 40mph. what portion of the total driving time did she spend driving 30mph?

  4/13

Step-by-step explanation:

Driving time is ...

  time = distance/speed

Then the ratio of times is ...

  6/20 : 6/30 : 6/40

  = 3/10 : 1/5 : 3/20

If we multiply by 20, we can get integer ratios:

  = 6 : 4 : 3

The middle ratio number represents the time spent at 30 mph, and the total of all ratio numbers represents the total driving time. Then the fraction spent at 30 mph is ...

  4/(6+4+3) = 4/13

Total driving time was 13/20 hours, or 39 minutes. Of that time, 12 minutes was spent driving at 30 mph.