How many minutes did it take to get home?

Question

An ant had to struggle to reach her hole at the top of 16 meter hill. Every 5 minutes she climbed 6 meters up the steep hill and slipped back 3 meters. How many minutes did it take to get home?

 

a. 20

b. 27

c. 30

d. 25

Answer 1

Make a table...

Minutes         climbed to      slipped back to    

5                        6                    3                         

10                      3+6=9          9-3= 6          

15                      6+6=12        12-3= 9

20                      9+6=15         15-3=12

25                      12+6=18         AT THE TOP so didn't slip back

 

So that was at 25 minutes.

 

Hope this organizational technique helped.

Answer 2

In 5 minutes the ant would travel 6 meters forward and 3 meters backwards for a net gain of 3 meters. This gets tricky, because, based on the wording of the problem, she is moving forward, then backwards, then forward, then backwards, with a gain of 3 meters each time.

 

In the first 5 minutes she would reach 6 meters before falling back.

In the second 5 minutes, she would climb from 3 to 9 before falling back to 6.

At the 15 minute mark she would have climbed to 12, and fallen back to 9.

At the 20 minute mark she would reach 15 and fall back to 12.

At the 25 minute mark she would have been able to make it from 15 meters to 16 meters with time to spare.

 

The temptation with this problem is to find the effective rate of 3 meters every 5 minutes, but that doesn't take into account the back and forth nature of her trip.