Question

An ant moved for several seconds and covered 3 mm in the first second
and 4 mm more in each successive second than its predecessor. If the
ant had covered 1 mm in the first second and 8 mm more in each
successive second, then the difference between path it would cover
during the same time and the actual path would be more than 6mm but
less than 30mm. Find the time for which the ant moved (in seconds)

Answer 1

3+4(t-1)=d
1+8(t-1)=c
|d-c|=a
6<a<30

These are the equations I came up with to solve this. =)

Answer 2

Typical it is!!!!

Answer 3

so what is the time ?

Answer 4

Just plug the equations in from the bottom to the top of how I listed them.

6<a<30
6<|d-c|<30
6<|3+4(t-1)-1-8(t-1)|<30
6<|6-4t|<30
time is positive, so we can only consider this case of the absolute value to fit within the range we want
6<4t-6<30
12<4t<36
3<t<9

So he could have walked for 4,5,6,7, or 8 seconds!

Answer 5

I suppose that the continuous range might be just as fine, for some reason I just assumed integer amounts at the end there.

Answer 6

but the option has

\(4\) as well as \(6\)

Answer 7

What's wrong with that?