Problem Solving

If Kaya travels 5 mph to work and twice as fast back home, she must travel 10 mph home.

Let's say that Kaya's work is x miles from her home - this means that she travels x miles to work and x miles back home.

We know that d = rt, or rearranged t =d/r. So we can express time to work as: x/5 and time back home as x/10. We also know that total time traveled = time to work + time back home, and that Kaya traveled 9 miles in total. This gives:

$$9=\frac{x}{5}+\frac{x}{10}$$

We can then simplify by multiplying each term by 10 and combining:

$$90=2x+x$$
$$90=3x$$
$$30=x$$

So the distance from Kaya's home to her work is 30 miles.

lheiannie07 wrote:It takes Kaya a total of 9 hours to go from home to work and back on her bike. She travels at an average speed of 5 miles per hour from home to work and twice as fast coming home than going to work. If Kaya travels by the same route in both directions then how many miles is the distance from her home to work?

A. 67.5
B. 45
C. 30
D. 18
E. 6

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