Any alberts in the house?!?! (Math)?

Question

A Grundo, a Gnorbu, a Gelert, and a Grarrl need to walk from Sakhmet to Qasala during a really bad heat wave. The heat is so bad, it's not possible to cross the open desert without some sort of shade. Fortunately, they have one umbrella. Unfortunately, however, only a maximum of two pets at a time can fit under the umbrella. The Grundo can cross the desert alone in 20 minutes. The Gnorbu can make the crossing alone in 16 minutes. The Grarrl can make the crossing alone in 8 minutes. And the Gelert can make the crossing in 4 minutes. Note that when two pets are making the crossing, they must do so at the pace of the slower pet!What is the minimum number of minutes that it will take for all of the pets to safely be together in Qasala?

Answer 1

52 min. is the minimum they would take to cross....

Grundo+Grarrl (up) = 20 .........(pace of Grundo)
Grarrl (down/back) = 4
Grarrl+Gnorbu (up) = 16 .........(pace of Gnorbu)
Grarrl (down) = 4
Grarrl + Gelert (up) = 8 .........(pace of Gelert)

Add the timings made, u'll get;

52 min.





TO make it simpler.......

any one person has to make a trip twice......

We know Algebraic addition of a+b=b+a

Thus the possible combinations are (keeping in mind the algebraic addition rule);

20+20+16+8+4 ;
20+16+16+8+4;
20+16+8+8+4;
20+16+8+4+4;

We don't even have to add them.... just by observation we can come to conclusion that the 4th combination will give us the minima...
thus the minimum timing made is 52 min.

Do let me know if its right....

Answer 2

You want the umbrella carrier to be the one that gets back in 4 minutes - so with that decided, Gelert takes Grundo for 20, back is 4, then Gelert takes Gnorbu for16, back for 4, then Gelert takes Grarri across for 8 and they're all there. TOTAL: 52 minutes

Answer 3

28 minutes
Grundo and Gnorbu together and Gelert and Grari together

Answer 4

Much too long! Leave them there!