Average speed question!!!?

Question

You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 73 km/h. On the way back you travel half the distance at 55 km/h and the other half at 73 km/h. What is your average speed from Houston back to San Antonio?

I am starting to get really frustrated with this problem. I keep getting 64 km/h as my answer but that is wrong.

Answer 1

Let D be the distance from San Antonio to Houston.

We know that rate = distance/time

So 55 km/hr = (D/2)/t1, where t1 is the time for the first half of the trip.

Then 73 km/hr = (D/2)/t2, where t2 is the time for the second half of the trip.

Since rate = distance/time, we know that 55 t1 = D/2 = 73 t2.

The average time is (t1 + t2)/2 = D/110 +D/146.

Hence, the average time is (146D + 110D)/(110)(146)

That equals 256D/(110)(146)

Hence, the average speed is D/average time =

D(110)(146)/(256D)=62.734375 km/hr

Answer 2

How long were you traveling?  

Answer 3

yes, your answer is wrong. you can't just take the average for speeds, it doesnt work like that.

to get the right answer, we'll say that the distance b/w the cities is 100 km. (you can put any number in, it doesnt matter) for the first 50 km, calculate how much time it took, and ditto for second 50 km.

now, you have the total time taken. if you add those two, and use the total distance(100 km), you can get avg. speed easily. (d=rt)