Hi All,

We're told that it takes Kaya a total of 9 hours in TOTAL to go from home to work and back on her bike and that 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. We're asked for the number of miles from her home to work. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, we know that her speed to work was 5 miles/hour and her speed coming home from work was 10 miles/hour. Since the TOTAL time spent traveling was exactly 9 hours (with no extra minutes or seconds), it's likely that the distance in each direction is a number that is evenly divisibly by 5 and 10, so the TOTAL distance will also be divisible by both 5 and 10. Based on the Answer choices, let's TEST Answer C first....

Answer C: 30 miles
IF the distance from Kaya's home to her work is 30 miles, then....
it would take (30 miles)/(5 miles/hour) = 6 hours to ride to work and
it would take (30 miles)/(10 miles/hour) = 3 hours to ride back home and
The TOTAL time would be 6 + 3 = 9 hours.
This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

swerve 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. Her rate is 5 mph when going from home to work, and her rate is twice as fast when coming home, which is 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