The problem in the image appears to be a word problem involving an automobile that covers a certain distance over three days. Let's break it down based on the given dataThe problem in the image appears to be a word problem involving an automobile that covers a certain distance over three days. Let's break it down based on the given

• An automobile travels a total distance of 168 km in 3 days.
• On the first day, it covers 30% of the total distance.
• On the second day, it covers 40% of the remaining distance.
• The third day covers the rest of the distance.

The problem asks: a) What distance was covered on the first day? b) What distance was covered on the second day? c) What percentage does the distance covered on the third day represent of the total distance covered in the first two days?

Let's calculate the answers step by step.

Step 1: Distance covered on the first day

The first day covers 30% of the total distance of 168 km: $\text{Distance on the first day} = 30\% \times 168 = 0.30 \times 168 = 50.4 \, \text{km}$

Step 2: Distance covered on the second day

The second day covers 40% of the remaining distance after the first day. The remaining distance after the first day is: $\text{Remaining distance} = 168 - 50.4 = 117.6 \, \text{km}$ The second day covers 40% of this remaining distance: $\text{Distance on the second day} = 40\% \times 117.6 = 0.40 \times 117.6 = 47.04 \, \text{km}$

Step 3: Distance covered on the third day

The remaining distance after the second day is: $\text{Remaining distance after the second day} = 117.6 - 47.04 = 70.56 \, \text{km}$ So, the third day covers 70.56 km.

Step 4: Percentage of the third day relative to the first two days

The total distance covered in the first two days is: $\text{Total distance (Day 1 + Day 2)} = 50.4 + 47.04 = 97.44 \, \text{km}$ Now, we calculate the percentage that the third day's distance represents compared to the distance covered in the first two days: $\text{Percentage of third day} = \left( \frac{70.56}{97.44} \right) \times 100 \approx 72.43\%$

Final Answers:

• a) The distance covered on the first day is 50.4 km.
• b) The distance covered on the second day is 47.04 km.
• c) The distance covered on the third day represents approximately 72.43% of the total distance covered in the first two days.

Would you like more details, or do you have any further questions?

Here are 5 related questions to deepen your understanding:

1. If the automobile traveled for 4 days, how would the problem change?
2. How would the result change if the second day covered 50% of the remaining distance instead of 40%?
3. What if the total distance was 200 km? How would the distance covered each day change?
4. What percentage of the total distance is covered in the first two days combined?
5. How can we express the total distance formula based on percentages?

Tip: Always verify if the total percentages add up to 100% when solving problems involving percentages over multiple intervals.