Question

If Lisa walks \(t\) blocks in 3 minutes, how many minutes will it take her to walk \(s\) blocks at the same rate?

Short answer

\(\frac{3s}{t}\) minutes

Step-by-step solution

Identify the Rate of Walking

First, identify the rate at which Lisa walks. The rate is the number of blocks she walks per minute. Given that Lisa walks t blocks in 3 minutes, the rate is \({\frac{t}{3}}\) blocks per minute.

Set Up the Equation for Walking s Blocks

Next, use the rate to find out how many minutes it will take Lisa to walk s blocks. The time to walk s blocks at her rate of \(\frac{t}{3}\) blocks per minute is given by \(\text{Time} = \frac{s}{\frac{t}{3}}\).

Simplify the Equation

To simplify \(\text{Time} = \frac{s}{\frac{t}{3}}\), multiply both sides to get rid of the fraction by flipping and multiplying. We have \(\text{Time} = s \times \frac{3}{t}\) which simplifies to \(\text{Time} = \frac{3s}{t}\).

Key concepts

time calculation

Calculating time, especially in relation to distance and speed, is a fundamental skill in mathematics. Understanding how to calculate time helps solve a variety of real-world problems, from planning travel schedules to organizing your day.
To find the time it will take Lisa to walk a certain distance, we need to know her walking rate and the distance she needs to cover. The rate we have is \[\frac{t}{3}\] blocks per minute.
Here is how to calculate:

• First, ensure you have the rate at which she walks.
• Then determine the total distance she needs to walk.
• Use the formula: \[\text{Time} = \frac{\text{Distance}}{\text{Rate}}\].

By plugging in the values mentioned above, you can easily calculate the time for any given distance.

distance formula

The distance formula is another key element when calculating the time required for travel. It connects the concepts of time, rate, and distance. The general format is:

• Distance = Rate \times\ Time.

In this particular exercise, you have the time and rate. You're solving for the distance initially to understand all walk scenarios.
For Lisa, who has a walking rate of \[\frac{t}{3}\] blocks per minute, we can reorganize the formula to solve for time if you have the distance:

basic algebra

Basic algebra involves manipulating equations to find unknown values, which is essential for solving many mathematical problems.
For this problem, let's break down the algebra used:

• First, we identify the rate: \[\frac{t}{3}\] blocks per minute
• Set up the equation for s blocks: \[\text{Time} = \frac{s}{\frac{t}{3}}\]
• Simplify the equation: multiply both sides by 3/t to get rid of the fraction.
• Final time formula: \[\text{Time} = \frac{3s}{t}\]

This process shows how algebra is used to transform and simplify equations for practical solutions.