# The Total Time Spent on the Trip is 9 hours.

• wowdusk
In summary, the man spent 4 hours walking and 1 hour for lunch, for a total of 5 hours. The time for the bus trip home was found to be 4/3 hours. Therefore, the total number of hours spent on the entire trip is 5 + 4/3 = 19/3 hours.
wowdusk

## Homework Statement

A man walks for 4 hours at the rate of x miles per hour. He stops an hour for lunch and then returns on a bus to his starting point. However, the bus travels at a speed 6 times that of his walking rate and follows a route that is twice as long. "What is the total number of hours spent on the entire trip?

D=rt

## The Attempt at a Solution

I know the man spent 4 hours on the first leg and had an hour lunch, so the total time is more than 5 hours. i was trying to manipulate the D=rt formula to fir this problem, but it wasn't coming out right. I would do 2(4x)/6x, for his time on the bus because it was twice the distance he walked (2(4x)) and moving at six times his speed (6x).

You are almost there with the answer. You key missing piece is how much time was spent on the bus trip home,...

You know 'going', 4 hours.
You know 'lunch', 1 hour.
You find an expression for TIME of bus trip home,
$$$time = \frac{{distance}}{{rate}}\quad = \;\;\frac{{2 \cdot 4 \cdot x}}{{6x}} = \frac{4}{3}\quad hours$$$

Finish the solution yourself now? Sum of three values.

## What is distance, rate, and time?

Distance, rate, and time are three important concepts in physics and mathematics that are used to calculate the speed at which an object is moving. Distance is the length between two points, rate (also known as speed) is the measure of how fast an object is moving, and time is the duration it takes for the object to travel a certain distance at a given rate.

## How do you calculate distance, rate, and time?

The formula for distance, rate, and time is d = r * t, where d is the distance, r is the rate, and t is the time. This means that to calculate any one of these variables, you will need to know the other two. For example, if you know the distance and rate, you can use the formula to find the time it takes to travel that distance.

## What is the difference between speed and velocity?

Speed and velocity are two related, but distinct concepts. Speed is a measure of how fast an object is moving, while velocity is a measure of both the speed and direction of an object's motion. In other words, velocity takes into account both the magnitude and direction of an object's movement, while speed only considers the magnitude.

## How does distance, rate, and time affect each other?

The relationship between distance, rate, and time can be summarized by the formula d = r * t. If any two variables are known, the third can be calculated using this formula. For example, if the distance and rate are known, the time can be calculated. Additionally, if the distance stays the same but the rate increases, the time will decrease, and vice versa.

## How is distance, rate, and time used in real life?

Distance, rate, and time are used in many real-life situations, such as calculating the speed of a car or airplane, determining the time it takes to travel to a destination, or estimating how long it will take to complete a task. These concepts are also important in fields such as physics, engineering, and transportation, where precise measurements of speed and time can greatly impact the outcome of a project or experiment.

• Precalculus Mathematics Homework Help
Replies
3
Views
2K
• Precalculus Mathematics Homework Help
Replies
3
Views
4K
• Precalculus Mathematics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Precalculus Mathematics Homework Help
Replies
15
Views
3K
• Precalculus Mathematics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
23
Views
497
• Precalculus Mathematics Homework Help
Replies
2
Views
2K
• Precalculus Mathematics Homework Help
Replies
6
Views
2K