Sure! Let's solve the problem step-by-step:
We are given that a man walked a total of 65 kilometers over 5 days, with each day walking 4 kilometers less than the previous day.
1. Define the variables:
- Let [tex]\( d_1 \)[/tex] be the distance walked on the first day.
- Since each day he walks 4 kilometers less than the previous day, the distances for the five days can be expressed as follows:
- Day 1: [tex]\( d_1 \)[/tex]
- Day 2: [tex]\( d_1 - 4 \)[/tex]
- Day 3: [tex]\( d_1 - 8 \)[/tex]
- Day 4: [tex]\( d_1 - 12 \)[/tex]
- Day 5: [tex]\( d_1 - 16 \)[/tex]
2. Form the equation for the total distance:
- The sum of the distances walked over the 5 days is equal to 65 kilometers.
- Therefore, we can write the equation:
[tex]\[
d_1 + (d_1 - 4) + (d_1 - 8) + (d_1 - 12) + (d_1 - 16) = 65
\][/tex]
3. Simplify the equation:
- Combine the like terms:
[tex]\[
d_1 + d_1 + d_1 + d_1 + d_1 - 4 - 8 - 12 - 16 = 65
\][/tex]
[tex]\[
5d_1 - (4 + 8 + 12 + 16) = 65
\][/tex]
[tex]\[
5d_1 - 40 = 65
\][/tex]
4. Solve for [tex]\( d_1 \)[/tex]:
- Isolate [tex]\( d_1 \)[/tex] by adding 40 to both sides of the equation:
[tex]\[
5d_1 = 65 + 40
\][/tex]
[tex]\[
5d_1 = 105
\][/tex]
- Divide both sides by 5:
[tex]\[
d_1 = 21
\][/tex]
5. Calculate the distance walked on the last day:
- The last day, the 5th day, is [tex]\( d_5 = d_1 - 16 \)[/tex]
[tex]\[
d_5 = 21 - 16
\][/tex]
[tex]\[
d_5 = 5
\][/tex]
So, the man walked 5 kilometers on the last day.
