Abby, Betty, Cassie, and Dale need to cross the river on a boat. The boat only fits at most two people. If two people go over one must bring it back for the others. Abby takes 1 min., Betty 2 min., Cassie takes 5 min., and Dale takes 10 min.. The time it takes is based on the longest time. For example if Abby and Dale go across that would take 10 min. Then if Abby comes back across that is an additional 1 min. totaling to 11 minutes thus far. What is the shortest amount of time needed to get everyone across the river?

Question

Reiny · Answer

This question makes little sense to me. Are the times given based on how long each one could row the boat?
Why would you let Dale row for 10 minutes, if Abby ran do it it 1 minute?
Anyway, taking your data at "face-value" ....

A=1
B=2
C=5
D=10

I would use A for all transfers
so:
(A+D+A) + (A+C+A) + A+B
= 11 + 6 + 2
= 19 MINUTES

Maddie · Answer

Actually, you can do it to only take 17 minutes. Betty takes Abby across, leaves her there, and rows back (4) Then Cassie and Dale row over together, and Abby takes the boat back (11) Then Abby and Betty row to the other side together(2)
Grand total: 17