# How Many Buses Departed While Jill Waited for Jack?

• recon
In summary, Jack and Jill have a daily meeting at a bus interchange where buses depart at equal intervals of time. On one occasion, Jill was 15 minutes late and Jack saw 6 buses depart. On another occasion, Jill was 26 minutes late and Jack saw 8 buses depart. When Jack was 43 minutes late, how many buses departed while Jill was waiting? To find all possible answers, one must explore the limits of the system by determining the maximum and minimum possible periods between buses for the first two criteria. By considering intervals of time that are just over and just under two bus periods long, this can provide insight into the limits on the period.
recon
Every day, Jack and Jill agree to meet at a certain time at the nearby bus interchange, where buses depart at equal periods of time. Once, Jill came 15 minutes later and Jack saw 6 buses depart. On a second occasion, Jill came 26 minutes later, and Jack saw 8 buses depart. On another occasion, Jack came 43 minutes later than Jill. How many buses departed the interchange while Jill was awaiting Jack?

I'm quite confused by this question at the moment. I've got to run now, and I may try and post my attempt a bit later, but I doubt I'm heading in the right direction.

Explore the limits of your system. What are the maximum and minimum possible periods between buses for each of the first two criteria? If I have an interval of time that's just over two bus periods long, how many buses can I fit inside it? If it's just under two bus periods long, how few buses can be fit inside? What does this tell you about the limits on the period?

No problem, let's break down the problem and see if we can come up with a solution together.

So, we have a scenario where Jack and Jill agree to meet at a certain time at the nearby bus interchange. The buses depart at equal periods of time, meaning they come and go at regular intervals.

On the first occasion, Jill came 15 minutes later than the agreed meeting time. During this time, Jack saw 6 buses depart.

On the second occasion, Jill came 26 minutes later and Jack saw 8 buses depart.

On the third occasion, Jack came 43 minutes later than Jill.

Now, we need to figure out how many buses departed while Jill was waiting for Jack.

To start, let's set up a variable to represent the number of buses that depart in a given time period. Let's call this variable "b".

On the first occasion, we know that Jack saw 6 buses depart. This can be written as 6b.

On the second occasion, Jack saw 8 buses depart. This can be written as 8b.

On the third occasion, Jack came 43 minutes later than Jill. This means that Jill was waiting for 43 minutes before Jack arrived. We can represent this as 43 minutes or 43/60 hours.

Now, we can set up an equation using the information we have:

6b = 43/60

We can solve for b by dividing both sides by 6:

b = 43/60 ÷ 6

b = 43/360

Now, we know that in one hour (or 60 minutes), 43/360 buses depart.

To find out how many buses departed while Jill was waiting for Jack, we need to find out how many buses depart in 15, 26, and 43 minutes.

For 15 minutes, we can set up a proportion:

15 minutes / 60 minutes = x buses / 43/360 buses

Solving for x, we get x = 6.45 buses.

For 26 minutes, we can set up a similar proportion:

26 minutes / 60 minutes = x buses / 43/360 buses

Solving for x, we get x = 11.73 buses.

And for 43 minutes, we know that 43/360 buses depart.

Therefore, while Jill was waiting for Jack

## What is an approximation math problem?

An approximation math problem is a type of mathematical problem where the goal is to find a close estimate or approximation of the solution, rather than the exact solution. This is often used in situations where finding the exact solution is either impossible or too time consuming.

## What are some common techniques used to solve approximation math problems?

Some common techniques used to solve approximation math problems include rounding, estimating, and using mathematical models or formulas. Other methods such as linearization, extrapolation, and interpolation may also be used depending on the specific problem.

## What are the benefits of using approximation in math problems?

Using approximation in math problems can save time and resources, as finding an exact solution can be time-consuming and difficult. It also allows for easier understanding and visualization of the problem, as well as providing a more practical solution in real-world scenarios.

## What are some real-world examples of approximation math problems?

One example of an approximation math problem is calculating the volume of a complex shape, such as a sculpture or a building, by breaking it down into simpler shapes and finding the approximate volume of each shape. Another example is estimating the number of people in a crowd by counting the number of people in a small section and using that as an approximation for the entire crowd.

## How can I improve my skills in solving approximation math problems?

To improve your skills in solving approximation math problems, practice using different techniques and methods, work on problems with varying levels of complexity, and seek help from resources such as textbooks, online tutorials, and math tutors. It is also important to have a strong understanding of basic mathematical concepts and formulas.

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