Calculating Average Speed of a Car Round Trip

[tigerlili]

Homework Statement

A car travels up a hill at a constant speed of 32 km/h and returns down the hill at a constant speed of 66 km/h. Calculate the average speed (in km/h) for the round trip.

Homework Equations

average speed= total distance/ delta time is the only equation i know for it

The Attempt at a Solution

there is no time, or actual distance given in this question, so i got confused and just tried to find the average from adding up the two speeds.. obviously that didn't work- this seems like a really simple problem, so where am i going wrong?

 

[CFDFEAGURU]

I don't think your doing anything wrong. I think the problem is missing the time information.

Thanks
Matt

 

[tigerlili]

but... it's online homework. that was just the given problem :/

 

[CFDFEAGURU]

Well, I have solved many dynamics problems and this problem is missing the information needed to solve it. Can you contact the teacher/instructor who posted it?

Thanks
Matt

 

[Vanadium 50]

CFDFEAGURU is, I fear, leading you astray. There is no missing fact, although there is a very important word, "returns". That means the distance up the hill is the same as the distance down the hill.

 

[CFDFEAGURU]

Whoops LOL. I missed that word.

Sorry to the OP.

Thanks
Matt

 

[tigerlili]

But.. it's average speed, not velocity.. so, direction doesn't matter, i thought? and you can't just average the speeds they give you.. and there's no time given :/

 

[Vanadium 50]

Suppose the distance is 1km. Work out average speed. 2km? 5km? See a pattern?

Now try x km.

 

[tigerlili]

so.. like, suppose 1 km is the distance

so do 32 km/hr / 1 km = 32 hr^-1 ,etc?

then what? :/ I'm sorry, i just really need this to be actually taught to me..

 

[Jebus_Chris]

Well, we know that
$$s=\frac{d}{t}$$
$$s=\frac{d_1+d_2}{t_1+t_2}$$
d1 and t1 are for the first have of the trip @ 32 km/h and d2 and t2 are for the other half at 66km/h.
Now you need to find what each of those are equal to.

 

[tigerlili]

but, how..

 

[Jebus_Chris]

$$d_1=d_2=x$$
$$v_1 = \frac{x}{t_1}$$
$$v_2 = x/t_2$$
Solve for the t's and plug into the speed equation in my last post. Then do some algebra.

 

[tigerlili]

so i have s= 2x/(x/32 + x/66)

but.. if we don't know what s is and we don't know what x is
what comes next?

 

[Jebus_Chris]

$$s=\frac{2x}{\frac{x}{32}+\frac{x}{66}}$$
If you find a common denominator for the lowed half of the equation the x's will cancel out.

 

[tigerlili]

yes, of course you're right

thank you very much for your help, i really appreciate it