Problem solving for time when average power and total energy is given

[Zunden]

Homework Statement

A student spends part of her day walking between classes or for recreation, during which time she expends energy at an average rate of 280 W. The remainder of the day she is sitting in class, studying, or resting; during these activities, she expends energy at an average rate of 120 W.

If she expends a total of 1.3×10^7 J of energy in a 24-hour day, how much of the day did she spend walking?

Knowns:

P1avg=280W
P2avg=120W
E=1.3*10^7J in one day.

Unknowns:

time spent walking.

Homework Equations

P=W/t
Pavg=W2-W1/t2-t1
Pint=dW/dt
1W=1J/s
??

The Attempt at a Solution

If total energy is 1.3*10^7J for the day, then that would mean Ptotal=1.3*10^7/86400s = 150.5W.
If this is the total power for the day how can she spend 280W walking in part of the day?

 

[supratim1]

Total work done = total energy spent = W (let)

let she spends 't' hours time walking, so rest time in class is '24-t' hours.

so, P1.t + P2.(24-t) = W.

solve and get answer.

 

[Zunden]

Thanks for the response. But when i plug numbers into that formula it gives me a time that is way too big to be right.

 

[supratim1]

covert the time in seconds.

 

[rwisz]

The average power for the entire day is not necessarily equal to the average power for the specific activity of walking. The 280W average power for walking only applies to the time spent walking, while the 120W average power for sitting, studying, or resting applies to the remainder of the day. Therefore, we cannot simply equate the total power for the day with the average power for walking.

To solve this problem, we can use the equation P=W/t, where P is power, W is work, and t is time. We know the average power for walking is 280W, so we can set up the equation as 280W = W/t_walking, where t_walking is the time spent walking. We also know the total energy expended in a day is 1.3*10^7J, so we can set up another equation as 1.3*10^7J = W/t_total, where t_total is the total time for the day.

Now, we can rearrange these equations to solve for t_walking and t_total:

t_walking = W/280W = 1.3*10^7J/280W = 46428.57 seconds
t_total = W/150.5W = 1.3*10^7J/150.5W = 86400 seconds

Therefore, the student spends 46428.57 seconds (or approximately 12.9 hours) walking in a 24-hour day.