Jennifer cut a board 2 m long into two pieces. One piece is 24 cm shorter than the other. Find the length of each piece.

A group of backpackers hiked 38 km over three days. The first day, they hiked 1 km less than 3 times as far as the second day. The third day, they hiked 2 km less than the first day. How far did they hike the first day.

I need equations.

long piece --- x

short piece -- x-24

x + x-24 = 24

solve for x
---------------
let distance of second day be x km
first day: <they hiked 1 km less than 3 times as far as the second day> ---> 3x - 1

third day ---> 2 less than first day
--->(3x-1) - 2

so:
3x-1 + x + (3x-1)-2 = 38

solve for x

23,164,20

Lime

To solve both problems, we need to set up equations based on the given information.

For the first problem, let's consider the length of the longer piece as x meters. According to the problem, the other piece is 24 cm shorter, which we can convert to meters by dividing by 100:

Length of the other piece = x - (24/100) meters
= x - 0.24 meters

Now, we know that the total length of the board is 2 meters:

x + (x - 0.24) = 2

Similarly, for the second problem, let's consider the distance they hiked on the second day as x km. According to the problem, the first day's distance is 1 km less than 3 times the second day's distance:

Distance hiked on the first day = 3x - 1 km

The third day's distance is 2 km less than the first day's distance:

Distance hiked on the third day = (3x - 1) - 2 km
= 3x - 3 km

The total distance hiked over three days is 38 km:

x + (3x - 1) + (3x - 3) = 38

These are the equations we can use to solve the problems.