Math Problem Statement

Tourists walked 3/4 of the total distance or 24 km. How many kilometers are left for him? By how many times is the distance walked greater than the remaining distance?

Solution

The question in Latvian can be translated as follows:

"A tourist walked 34\frac{3}{4} of the total distance or 24 km. How many kilometers are left for the tourist to walk? By how many times is the distance walked greater than the remaining distance?"

To solve this:

  1. Finding the total distance:
    If 34\frac{3}{4} of the total distance is 24 km, we can let the total distance be xx kilometers. Thus, we have the equation: 34x=24\frac{3}{4}x = 24 Solving for xx: x=24×43=32kmx = 24 \times \frac{4}{3} = 32 \, \text{km} So, the total distance is 32 km.

  2. Distance left to walk:
    The tourist has walked 24 km, so the remaining distance is: 3224=8km32 - 24 = 8 \, \text{km}

  3. Comparing the distance walked to the remaining distance:
    The tourist walked 24 km and the remaining distance is 8 km. To find how many times the walked distance is greater than the remaining distance: 248=3\frac{24}{8} = 3 The distance walked is 3 times greater than the remaining distance.

Summary:

  • The tourist has 8 km left to walk.
  • The distance walked is 3 times greater than the remaining distance.

Would you like further details or clarification on any part? Here are 5 related questions to deepen your understanding:

  1. How would the solution change if the tourist had walked 23\frac{2}{3} of the total distance?
  2. How can we generalize the formula for different fractions of a journey completed?
  3. What would happen if the total distance were not known and only a fraction of the remaining distance was given?
  4. How could this type of problem be applied to time or fuel consumption in a real-life scenario?
  5. If the tourist walked half the remaining distance after this, how far would they have left?

Tip: Always verify the relationship between the fraction given and the total distance when solving proportional problems.

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Math Problem Analysis

Mathematical Concepts

Proportions
Fractions
Algebra

Formulas

3/4 * total distance = 24 km
remaining distance = total distance - walked distance
comparison = walked distance / remaining distance

Theorems

Proportion Calculation

Suitable Grade Level

Grades 5-7