# Why total time taken s₁/v₁ + s₂/v₂ + s₃/v₃ in average speed?

## Homework Statement

As we know the Average speed = Total distance / Total time but why in the case below
Distance traveled = s₁ + s₂ + s₃ and total time taken = s₁/v₁ + s₂/v₂ + s₃/v₃ How is it possible? so, altogether
Vav = s₁ + s₂ + s₃ / ( s₁/v₁ + s₂/v₂ + s₃/v₃)

## The Attempt at a Solution

I only know (Average speed = Total distance / Total time)

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Doc Al
Mentor
The total time is the sum of the times for each segment, which you can calculate (as shown) given the speed and distance in each segment.

Stephen Tashi
How is it possible?
What do you mean by "it"? What question does the problem ask?

so, altogether
Vav = s₁ + s₂ + s₃ / ( s₁/v₁ + s₂/v₂ + s₃/v₃)
Perhap you meant $V_{av} = (s_1 + s_2 + s_3)/ ( s_1/v_1 + s_2/v_2 + s_3/v_3)$.

You didn't explain the variables. My guess is that the problem states that an object travels distance $s_i$ at average velocity $v_i$ for $i =1,2,3$.

What do you mean by "it"? What question does the problem ask?

Perhap you meant $V_{av} = (s_1 + s_2 + s_3)/ ( s_1/v_1 + s_2/v_2 + s_3/v_3)$.

You didn't explain the variables. My guess is that the problem states that an object travels distance $s_i$ at average velocity $v_i$ for $i =1,2,3$.
It means total time taken 's₁/v₁ + s₂/v₂ + s₃/v₃' How is it possible?

The total time is the sum of the times for each segment, which you can calculate (as shown) given the speed and distance in each segment.

Doc Al
Mentor
If you're given a distance and speed for an interval, how would you find the time taken to cover that distance at the given speed?

If you're given a distance and speed for an interval, how would you find the time taken to cover that distance at the given speed?
That's what I want to learn. Please explain

Doc Al
Mentor
That's what I want to learn. Please explain

Solve for time.

Solve for time.
Time = distance / speed

If you're given a distance and speed for an interval, how would you find the time taken to cover that distance at the given speed?
Now I got it what you mean.

Solve for time.

Doc Al
Mentor
That's a very specialized formula. Consider something moving from point A to point B at speed v1 and then back to A at speed v2. Now can you figure it out?

That's a very specialized formula. Consider something moving from point A to point B at speed v1 and then back to A at speed v2. Now can you figure it out?
Still, I don't understand what you mean. get your point a little bit easier. how do we get '2v₁v₂' in the place of distance and why do we add '(v₁ + v₂)' in the place of time?

jbriggs444
Homework Helper
2019 Award
Still, I don't understand what you mean. get your point a little bit easier. how do we get '2v₁v₂' in the place of distance and why do we add '(v₁ + v₂)' in the place of time?
Try following @Doc Al's suggestion. Let d be the distance from point A to point B. Write down a formula for the average velocity: total distance divided by total time. Show us that formula.

Try following @Doc Al's suggestion. Let d be the distance from point A to point B. Write down a formula for the average velocity: total distance divided by total time. Show us that formula.
Vavg = d / t

jbriggs444
Homework Helper
2019 Award
Vavg = d / t
First, a round trip does not have distance = d. Now write that "t" in terms of d, v1 and v2

First, a round trip does not have distance = d. Now write that "t" in terms of d, v1 and v2
like this equeation Vavg = t v₁v₂ / t?

jbriggs444
Homework Helper
2019 Award
like this equeation Vavg = t v₁v₂ / t?
That equation makes no sense. If points A and B are distance d apart, how much time does it take to get from A to B at speed v1?

That equation makes no sense. If points A and B are distance d apart, how much time does it take to get from A to B at speed v1?
I think t1 time required

jbriggs444
Homework Helper
2019 Award
I think t1 time required
One more try and then I'm out. Please write a formula for t1 that uses only d and v1

One more try and then I'm out. Please write a formula for t1 that uses only d and v1
Yes t1 = d / v1

jbriggs444
Homework Helper
2019 Award
Yes t1 = d / v1
OK. Now repeat for t2, the time for the return trip.
Then write down a formula for the total time taken for the round trip.
Finally, write down a formula for the average velocity over the round trip using only d, v1 and v2.

OK. Now repeat for t2, the time for the return trip.
Then write down a formula for the total time taken for the round trip.
Finally, write down a formula for the average velocity over the round trip using only d, v1 and v2.
t1 + t2 = d / v1 + d / v2, t = d (v1 + v2) / v1v2, Vavg = d / t = d / d(v1 + v2) / v1v2 = v1v2 / v1 + v2 [ but the equeation is 2v1v2 / v1 + v2] Could you check my calculation please?

Stephen Tashi