A girl leaves her home A at 9am, and after cycling for 25km at 5km/h she reaches her destination B at 2pm. After having lunch at B for 90 minutes, she sets off for home. On the way home she stops for half an hour to see a friend who lives at C, which is 10km from A. At 5:30pm, she leaves C and cycles until she reaches home at 7pm.

a) What was the girls speed from B to C?
b) What was her speed from C to home?

what's the problem? Just calculate the distance and time as needed, and the average speed is distance/time.

For (a),
A-B is 25km
A-C is 10km
So, B-C is 15km

C-A takes 1.5 hr
B-A takes 3.5 hr
stop at C takes 0.5 hr
So, the B-C leg takes 1.5 hr

15km/1.5hr = 10km/hr

The rest is now easy, given the above data.

To find the girl's speed from B to C and from C to home, we can use the formula: speed = distance / time. Let's break down the given information step by step.

a) What was the girl's speed from B to C?
First, we need to find the total time she spent traveling from B to C. We know that she reached B at 2pm and had lunch for 90 minutes, so she left B at 2pm + 1.5 hours = 3:30pm.

Next, we need to determine the distance between B and C, which is given as 10km.

To find the speed, we divide the distance by the time taken. The time taken from B to C is from 3:30pm to 5:30pm, which is 2 hours.

Therefore, the girl's speed from B to C is: speed = distance / time = 10km / 2 hours = 5km/h.

b) What was her speed from C to home?
To find the girl's speed from C to home, we need to calculate the distance and time taken for this leg of the journey separately.

The distance from C to home is the same as the distance from A to C, which is given as 10km.

The girl left C at 5:30pm and reached home at 7pm, which is a time difference of 1.5 hours.

Using the formula, we divide the distance by the time taken: speed = distance / time = 10km / 1.5 hours = 6.67 km/h.

Therefore, the girl's speed from C to home is approximately 6.67 km/h.