How do i find the average speed for his question: "A bicycle racer rides from a starting marker at 10m/s. She then rides back along the same rout from the turnaround marker at 16m/s. What is her average speed for the whole race?"

Question

anonymous · Answer

well my book says you have to use speen and velocity

anonymous · Answer

I get that, (y2-y1/x2-x1) but theres no info in the question about the actual amount of distance traveled or actual time it took to travel

anonymous · Answer

You may be able to add both velocities up and divide them up by how many there are so, $$\frac{ v_1+v_2 }{ 2 }$$

anonymous · Answer

I thought of that, but the book im using said that that is incorrect and the answer is actually 12m/s, not 13m/s like you and i thought

anonymous · Answer

Find all the distances. Average Speed is ALWAYS total distance/total time.

anonymous · Answer

Assuming you have the times taken. Is that the whole question?

anonymous · Answer

Yeah, that's the entirety of the question.

anonymous · Answer

We can substitute values around to come up with in that equation to give, 
$$\frac{ 2v_1+v_2 }{ (v_1+v_2) }$$

anonymous · Answer

but that gives 1.384, not 12m/s as the book's answer states

anonymous · Answer

Sorry the addition sign is not suppose to be there its all multiplied at the top

anonymous · Answer

$$\frac{ 2v_1v_2 }{ (v_1+v_2) }$$

anonymous · Answer

Eureka! Thank you!

anonymous · Answer

My pleasure

anonymous · Answer

Good work, John.

anonymous · Answer

I believe that solves your question! Please mark the question as Closed. Thanks :)