# Running and Walking Question

yeahman68
A man is running and walking a distance of 2 km. He will walk for 1 km and run for 1 km. At the end, his average velocity was recorded to be 15 km/hr. His running velocity is twice that of his walking velocity. What was his walking speed?

The answer was recorded to be 7.5 km/hr, but cannot figure it out unfortunately.

This is how I attempted to do the problem:

Equation relating the two velocities: time = 1/2(Distance/Velocity of walking) + 1/2(Distance/Velocity of running)

Average Velocity=Total Distance/Total Time

15 km/hr= 2 km / x hours x= (2/15) hr or (.1333333333 hr)

Tried doing things past this point but cannot get the correct answer.

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Mentor
A man is running and walking a distance of 2 km. He will walk for 1 km and run for 1 km. At the end, his average velocity was recorded to be 15 km/hr. His running velocity is twice that of his walking velocity. What was his walking speed?

The answer was recorded to be 7.5 km/hr, but cannot figure it out unfortunately.

This is how I attempted to do the problem:

Average Velocity=Total Distance/Total Time

15 km/hr= 2 km / x hours x= (2/15) hr or (.1333333333 hr)

Tried doing things past this point but cannot get the correct answer.

Welcome to the PF.

You are doing fine so far. You need to write one more equation, to express the fact that you are given with the relatinoship between the two velocities. Given that equation and what you have so far, you should be able to solve the problem. Show us your work going forward now...

yeahman68
Thank you for your input. I have given my proposed equation relating time and the 2 variables. Here is the work I have continuing from the top:

Since the time is coming from two velocities:

.133333333 hours = (1 km/velocity of running) + (1km/velocity of walking)

I guess you can express the velocity of running as twice that of walking.

Thus,

Using the equation relating the variables:

.13333333 hours = (2/ velocity of walking) + (2/2 velocity of walking)

.13333333 hours = (2 km/velocity of walking) + (2 km/2 velocity of walking)

If my work looks right:

.1333333333 hours = (2 km/velocity of walking) + (1 km/velocity of walking)

.1333333333 hours = 3 km/velocity of walking

Velocity of walking = 22.5 km/hr ???????????????????????? So frustrated.

azizlwl
I think there is error in the answer given.

If the walking pace is 7.5km/hr and running is 15 km/hr then total time is 1/7.5 hr and 1/15hr respectively.
Average will be 2/0.2= 10km/h
Another logic, how can average equal to highest speed when lesser speed present.

Let x be the walking speed,
xt1=1/2 ......(1)
xt2=1 .......(2)
2/(t1+t2)=15 ......(3)

x=11.25km/hr

Check.

2/(1/11.25+1/22.5)=15

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yeahman68
Okay Thank You. I will bring this up with my professor tomorrow.

Bhumble
It is impossible for all values to be equal to or less than the average, except with negligible times and rounding errors...

yeahman68
The answer is 11.25 km/hr for the walking velocity. My TA told me the answer for another version of the quiz where the values were different. False Alarm! Thank You for all who helped me out.