Math Problem Statement

A car travels a fixed distance of 260km. A formula for finding the average speed of the car, s (km)/(h), when it takes t hours to travel this distance is s=(260)/(t). Find the time taken for a car to travel this distance at a speed of (100km)/(h).

Solution

To find the time tt taken for a car to travel a distance of 260 km at a speed of 100 km/h, you can use the formula:

s=260ts = \frac{260}{t}

Given that the speed ss is 100 km/h, you can set up the equation:

100=260t100 = \frac{260}{t}

Now, solve for tt:

  1. Multiply both sides of the equation by tt to eliminate the denominator:

100t=260100t = 260

  1. Divide both sides by 100 to isolate tt:

t=260100t = \frac{260}{100}

  1. Simplify the fraction:

t=2.6 hourst = 2.6 \text{ hours}

So, the time taken for the car to travel the distance of 260 km at a speed of 100 km/h is 2.6 hours.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

  1. How would the time change if the speed were reduced to 80 km/h?
  2. What would be the average speed if the car took 3.25 hours to cover 260 km?
  3. How can you express the time in minutes instead of hours?
  4. If the car made a 20-minute stop during the trip, what would be the new average speed?
  5. How would you modify the formula if the distance was not fixed?

Tip: Always keep track of the units when solving problems involving speed, distance, and time. It helps avoid errors and ensures accurate calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Ratio and Proportion

Formulas

s = 260 / t

Theorems

Basic Proportionality Theorem

Suitable Grade Level

Grades 6-8