on a trip Liam agreed to drive 2/3 of the total distance if Jessica drove the remaining distance. Upon completing his share of driving, Liam fell asleep. When Liam awoke, Jessica still had 20% of her share left to drive. In lowest terms, for what fractional part of the whole trip was Liam asleep.

So, Amber, if she has 20% left, she's driven 80%, right?

80/100 = 4/5

We also know she agreed to drive the last 1/3 of the total, so she drove 4/5 of her 1/3 while he slept.

(4/5)(1/3) = 4/15

Hope this helps!