# Running / walking for half distance

• sp3sp2sp
In summary, Robin walks the entire distance in 2.5 hours, while Arthur only walks half of the distance in 1.5 hours.

## Homework Statement

Arthur and Robin both can run at speed v_r and walk at speed v_w, with v_r > v_w. They set off together on a journey of distance D. Robin walks half of the distance and runs the other half. Arthur walks half of the time and runs the other half.

How long does it take Robin to cover the distance D?

Express the time taken by Robin in terms of v_r, v_w, and D.

## Homework Equations

v = d/t and t = d/v

## The Attempt at a Solution

total time = (D/2)/(v_w) + (D/2)/(v_r)

= D/(2v_w) + D/(2v_r)

I just wanted to check before I submit this , thanks for any help

Last edited:
Nope. If t = D/v, then D/(2vw) is the time it takes to cover distance D/2 with walking speed vw and likewise for the running time in your expression. What you have is Arthur's total time, not Robin's.

Thanks for the response I got the names mixed up and I edited my first post. Got the first part correct.

The next question is
"Find Robin's average speed for covering the distance D.
Express Robin's average speed in terms of vr and vw".

v_avg = D / [(D/2v_w) + (D/2v_r)]
= 1 / [(1/2v_w) + (1/2v_r)]

= 2v_w + 2v_r

that last simplification I am not sure about though.. Thanks for any more help

sp3sp2sp said:
Thanks for the response I got the names mixed up and I edited my first post. Got the first part correct.

The next question is
"Find Robin's average speed for covering the distance D.
Express Robin's average speed in terms of vr and vw".

v_avg = D / [(D/2v_w) + (D/2v_r)]
= 1 / [(1/2v_w) + (1/2v_r)]
The above is correct.

The following line is not correct.
= 2v_w + 2v_r

that last simplification I am not sure about though.. Thanks for any more help
Multiply the numerator and denominator of ##\displaystyle \ \frac {1}{\displaystyle \frac{1} { 2v_w }+\frac{1} { 2v_r } } \ ## by ##\displaystyle \ 2 v_w v_r \,. ##

## 1. What is the difference between running and walking for a half distance?

Running and walking for a half distance refer to the specific distance covered in a race, with half distance typically being 13.1 miles or 21.1 kilometers. The main difference between the two is the speed at which they are completed. Running typically involves a faster pace and higher intensity, while walking is done at a slower pace and lower intensity.

## 2. How long does it take to run or walk a half distance?

The time it takes to run or walk a half distance can vary greatly depending on individual fitness levels, training, and race conditions. On average, it can take anywhere from 1.5 to 3 hours to complete a half distance race.

## 3. Is it better to run or walk a half distance?

Both running and walking have their own benefits and it ultimately depends on individual goals and preferences. Running can provide cardiovascular and muscular benefits, while walking can be a lower impact option for those with joint or mobility issues. It is recommended to listen to your body and find the best approach that works for you.

## 4. What is the best training plan for running or walking a half distance?

The best training plan for running or walking a half distance will depend on your current fitness level and goals. It is important to gradually increase mileage and incorporate rest days to prevent injury. Consulting with a certified running or fitness coach can also help create a personalized training plan.

## 5. How can I prepare for a half distance race?

To prepare for a half distance race, it is important to have a consistent training plan, including both running and strength training. It is also crucial to properly fuel your body with a balanced and nutritious diet. On race day, make sure to hydrate well and have a positive mindset. It can also be helpful to familiarize yourself with the race course and have a race day strategy.