# Average Speed Question

• Feb 3rd 2010, 06:07 PM
mmattson07
Average Speed Question
Hi, I am having trouble getting started on this physics problem...it seems fairly simple just need some hints:

You drive on Interstate 10 from San Antonio to Houston, half the time at 73 km/h and the other half at 90 km/h. On the way back you travel half the distance at 73 km/h and the other half at 90 km/h. What is your average speed a) from San Antonio to Houston, b) from Houston back to San Antonio, and (c) for the entire trip?

I know average speed is the total distance during the trip divided by the total time for the trip but I am not sure how to determine those.

Thanks.
• Feb 4th 2010, 11:24 AM
Soroban
Hello, mmattson07!

This was trickier than I thought . . .

Quote:

You drive on Interstate 10 from San Antonio to Houston,
half the time at 73 km/h and the other half at 90 km/h.

On the way back you travel half the distance at 73 km/h and the other half at 90 km/h.

(a)What is your average speed from San Antonio to Houston?

For convenience, assume that the distance from San Antonio to Houston is 1314 km.

We drove $\displaystyle x$ km at 73 mph.
. . This took: .$\displaystyle \frac{x}{73}$ hours.

We drove the other $\displaystyle 1314-x$ km at 90 mph.
. . This took: .$\displaystyle \frac{1314-x}{90}$ hours.

These two times are equal: .$\displaystyle \frac{x}{73} \:=\:\frac{1314-x}{90} \quad\Rightarrow\quad x \:\approx\:588.48$ km.

We drove 588.48 km at 73 km/hr.
. . This took: .$\displaystyle \frac{588.48}{73} \:\approx\:8.06$ hours

We drove the other: .$\displaystyle 1314 - 588.48 \,=\,725.52$ km at 90 km/hr.
. . This took: .$\displaystyle \frac{725.52}{90} \;\approx\:8.06$ hours. .(Of course!)

We drove 1314 km in 16.12 hours.

From San Antonio to Houston, we averaged: .$\displaystyle \frac{1314}{16.12} \:\approx\:81.51$ km/hr.

Quote:

(b) What is your average speed from Houston back to San Antonio?

We drove 657 km at 73 km/hr,
. . This took: .$\displaystyle \frac{657}{73} \:=\:9$ hours.

We drove 657 km at 90 km.hr.
. . This took: .$\displaystyle \frac{657}{90} \:=\:7.3$ hours.

We drove 1314 km in 16.3 hours.

From Houston to San Antonio, we averaged: .$\displaystyle \frac{1314}{16.3} \:\approx\: 80.61$ km/hr.

Quote:

(c) What is your average speed for the entire trip?

We drove a total of 2628 km in a total of 32.42 hours.

For the entire round trip, wel averaged: .$\displaystyle \frac{2628}{32.42} \;\approx\;81.06$ km/hr.