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

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

by swerve » Tue Apr 24, 2018 10:31 am

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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

The OA is C.

Please, can anyone explain this PS question? I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Apr 24, 2018 10:31 am

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by GMATGuruNY » Tue Apr 24, 2018 10:54 am

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

Time and rate have a RECIPROCAL RELATIONSHIP:
If John's time is twice Mary's time, then John's rate is 1/2 Mary's rate.

Here, the rate for the return trip is twice the rate for the trip to work, implying that the time for the return trip is 1/2 the time for the trip to work.
Since the total time for both trips is 9 hours, we get:
Trip to work = 6 hours.
Return trip = 3 hours.

Since the 6-hour trip to work is traveled at 5 mph, the distance = rt = 5*6 = 30 miles.

The correct answer is C.

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by [email protected] » Tue Apr 24, 2018 9:59 pm

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

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Rich

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Apr 26, 2018 2:49 pm

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

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