It takes Kaya a total of 9 hours to go from home to work and back on

can be solved using ratio,,

speed ratio is 5:10 or 1:2
time ratio will be 2:1.. in a total of 9 hours,,
6 hours for going and 3 hours for coming back,,

distance = 5* 6 = 30

ans C

as K's speed ratio going/returning is 5:10, or 1:2,
her time ratio going/returning is 2:1, or 6:3
5 mph*6 hrs=30 miles distance
C

home to office speed=5 kmph
office to home speed= 5*2= 10 kmph
Time=Distance/speed
D/5 + D/10 = 9
D= 30
Answer: C

We are given that Kaya takes a total of 9 hours to make the round trip from home to work and back home. She has a rate of 5 mph when going from home to work, and her rate is twice as fast when coming home, so 10 mph.

If we let the distance between home and work = d, then her time from home to work is d/5 and her time from work to home is d/10. Since the total time is 9 hours, we can create the following equation to determine d:

d/5 + d/10 = 9

Multiplying the entire equation by 10, we have:

2d + d = 90

3d = 90

d = 30

Alternate Solution:

Let’s denote the time it takes Kaya to go back home from work as t. Since Kaya travels twice as fast going home, the time it takes for her to go to work is twice as long as the time to go home, i.e. 2t. We are given that the total time is 9 hours, thus t + 2t = 3t = 9 and t = 3. Since it takes 2t = 6 hours at 5 mph to go to work, the distance is 6 x 5 = 30 miles.

Answer: C

Avg speed formula = 2s1s2/s1+s2

D = 20/3 * 9
D=3

D/9 = D/(D/5 + D/10)

10/3 = D/9

D = 90/3 ----> 30

Let the distance between home and office be 'x' miles

Time = \(\frac{Distance}{Speed}\)

Speed at which she travels from home to office = 5 mph
Speed at which she travels from office to home = 10 mph

Time taken = 9hrs = \(\frac{x}{5}\) +\(\frac{x}{10}\)

x = 30 miles

My way of solving the above question