Calculate Snail's Daily Distance: 3 Days, 40 Meters Back

Q: How do I know which direction is positive?

Choose forward movement as positive and backward as negative. Since the snail returns to start, the net displacement is zero: forward distance - backward distance = 0.

Q: What if I set up the equation differently?

You could write 3x + 5x - 40 = 0, which gives the same result! Both setups work as long as you're consistent with positive/negative directions.

Q: Can the distance be negative?

No! Distance is always positive. If you get a negative answer, check your equation setup - you might have mixed up the directions.

Q: How do I verify my answer makes sense?

Check that forward distance equals backward distance: 3(5) + 5(5) = 15 + 25 = 40 meters forward, and 40 meters backward. The snail returns exactly to start! ✓

Linear Equations with Distance Variables

A snail travels across several set distances each day. On the first day, it crosses 3 such distances and on the second day it covers 5 such distances. On the third day, it goes backwards 40 meters and reaches its starting point.

What is the length of each set distance the snail crosses?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Define the distance the snail travels each time as a variable.
Step 2: Set up an algebraic equation reflecting the snail's total movement.
Step 3: Solve the equation for the unknown variable.

Now, let's work through each step:
Step 1: Let $x$ represent the length of each set distance.
Step 2: The total forward distance over the first two days is $3x + 5x = 8x$ .
The backward movement on the third day is 40 meters.
Since the snail ends up at the starting point, the equation is $8x = 40$ .
Step 3: Solve for $x$ :
$8x = 40 \implies x = \frac{40}{8} = 5$

Therefore, the solution to the problem is $x = 5$ meters.

Final Answer

5 meters

Key Points to Remember

Essential concepts to master this topic

Setup: Define unknown distance as variable, track total movement
Technique: Forward distance 3x + 5x = 8x equals backward 40m
Check: Substitute x = 5: 8(5) = 40 meters total ✓

Common Mistakes

Avoid these frequent errors

Adding backward distance instead of subtracting
Don't write 3x + 5x + 40 = 0 for total movement! The snail goes backward 40m to return to start, so forward distance must equal backward distance. Always set forward movement equal to backward movement: 8x = 40.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why does the snail end up at the starting point?

The problem states that after going backward 40 meters on day 3, the snail reaches its starting point. This means the total forward distance from days 1 and 2 exactly equals the 40-meter backward movement.

How do I know which direction is positive?

Choose forward movement as positive and backward as negative. Since the snail returns to start, the net displacement is zero: forward distance - backward distance = 0.

What if I set up the equation differently?

You could write 3x + 5x - 40 = 0, which gives the same result! Both setups work as long as you're consistent with positive/negative directions.

Can the distance be negative?

No! Distance is always positive. If you get a negative answer, check your equation setup - you might have mixed up the directions.

How do I verify my answer makes sense?

Check that forward distance equals backward distance: 3(5) + 5(5) = 15 + 25 = 40 meters forward, and 40 meters backward. The snail returns exactly to start! ✓

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime