a woman drives to work and averages 70 kilometers per hour for the trip. On her trip from work to home she averages 100 kilometers per hour. What is her average speed for the round trip?

average speed = total distance/total time

we don't know how far it is to her place of work,
let that distance be x

time on first part = x/70
time for return trip = x/100
total time = x/70 + x/100
= 17x/700

avg speed = 2x/(17x/700)
= 2x(700/17x)
= 1400/17 km/h
or appr 82.4 km/h

To find the average speed for the round trip, we need to calculate the total distance traveled and the total time taken. Let's break down the problem into steps:

1. Let's assume the distance from her home to work is 'x' kilometers.
2. On the trip to work, she travels 'x' kilometers at an average speed of 70 kilometers per hour. So, the time taken for this trip is x/70 hours.
3. On the trip back home, she again travels 'x' kilometers, but at an average speed of 100 kilometers per hour. So, the time taken for this trip is x/100 hours.
4. The total distance traveled in the round trip is '2x' kilometers (x kilometers to work + x kilometers back home).
5. The total time taken for the round trip is (x/70 + x/100) hours.

To find the average speed, we divide the total distance by the total time:

Average Speed = Total Distance / Total Time

Average Speed = 2x / (x/70 + x/100)

Simplifying the expression:

Average Speed = 2x / (10x/700 + 7x/700)

Average Speed = 2x / (17x/700)

Average Speed = (2x * 700) / 17x

Average Speed = 1,400 / 17

Therefore, the woman's average speed for the round trip is approximately 82.35 kilometers per hour.