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12 Days of Christmas GMAT Competition 2025 - Day 1: At 10:00 p.m.

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Bunuel

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15 Dec 2025, 09:00

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At 10:00 p.m., a cyclist is 10 miles from home on a straight road. From that time on, the cyclist continues riding farther from home at a constant speed of 3 minutes per mile, then turns around and rides back toward home at the same speed along the same road. If the cyclist must arrive back home at 10:48 p.m., how many additional miles can the cyclist travel away from home after 10:00 p.m. before turning around?

A. 2
B. 3
C. 6
D. 9
E. 12

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Bunuel

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15 Dec 2025, 10:00

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Bunuel

GMAT Club Official Explanation:

At 10:00 p.m., the cyclist is 10 miles from home. On the way back, riding those 10 miles at 3 minutes per mile will take 30 minutes. Since the cyclist must be home at 10:48 p.m., only 18 minutes remain for riding farther away and then returning to the 10-mile point. That gives 9 minutes out and 9 minutes back. At a pace of 3 minutes per mile, 9 minutes corresponds to 3 miles.

Answer: B.

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15 Dec 2025, 09:06

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in 48 mins the rider can ride 16 miles (48/3)
10 + x + x = 16
x =3

Zosima08

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15 Dec 2025, 09:07

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The cyclist has a total time left of 48 mins and he rides at 3min/mile. So he has 48/3= 16 miles total to ride until time runs out.
Since he is 10 miles away from home and he can ride 16 more then the total is 26 miles. Divide 26 by 2 = 13 miles away from home and 13 miles back. So 3 miles is the answer

Bunuel

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15 Dec 2025, 09:07

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Let the additional miles be x
Distance the cyclist travel before returning home is x away from home, x+10 towards home
So total distance = 2x+10

Speed = 3minutes/mile => 1/3 miles/min
Time = 48mins

Since speed is constant
2x+10/48 = 1/3
2x+10 = 16
2x=6
x=3

Bunuel

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15 Dec 2025, 09:08

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speed=dist/time=48/3
since the travel'ser is moving away and is initially 10 mile to total distance will be:
10+2x=16
x=3

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15 Dec 2025, 09:10

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Speed= 3 min for 1 mile i.e. 1 min for 1/3 mile
so for 48 min, 48/3 = 16 miles is the total distance travelled from 10:00 pm till 10:48pm
Let x be the distance travelled away from home. (Let starting point be A, Farthest point from home, before turning back be B )
total distance travelled ( A to B + B to A + A to home) = x + x + 10 = 16
This gives x= 3

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15 Dec 2025, 09:11

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Final Answer is 3 miles

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15 Dec 2025, 09:12

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Dont get confused by language of 3 minute per mile.

10 miles basis the ratio is 30 minutues so additional 18 minutes available which translates to 18/3 = 6 miles and since it will be two way divide it by 2 to get the answer of 3 miles each side.

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15 Dec 2025, 09:13

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So initially, at 10:00 pm, a cyclist is at 10 m away from home and continue ride farther at 3 min/mile. Also that cyclist has to return back at home by 10:48 pm.

Let's assume a cyclist rides "x" mile farther

That means a cyclist has to travel x + x + 10 miles within 48 minutes.

To cover 10 miles, it will take 3 (min/m) * 10 = 30 minutes.

So a cyclist needs to travel x + x = 2x in 18 minutes .

In 18 minutes it can ride 6 miles

So 2x = 6 miles
x = 3 miles.

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15 Dec 2025, 09:13

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The cyclist have 48 mins to go and come back home.
He rides at constant speed of 3 mins per mile.
Let, Time taken to ride away from home = 3x mins
Distance covered from home to the turning point = (10+x) miles
Time taken to ride back home = 3(10+x) min
Total time taken = 48 mins = Time taken to ride away from home + Tim taken to ride back home
3x + 3(10+x) =48 mins
3x +30 +3x =48
6x=48-30=18
x=18/6=3 miles

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15 Dec 2025, 09:13

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the answer is 6 miles

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15 Dec 2025, 09:16

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First thing first, will need to note that the cyclist is 10miles AWAY from home. To find out how many more miles he can ride, we can easily calculate that as 48 minutes / 3 minutes per mile to being 16 miles he can ride within that time.

So adding the initial 10 miles with the 16, we can see that his total ride distance will be 26 miles, or rather 2d, since the total trip would be d * 2.

2d = 26 miles; 26 / 2 = 13; d = 13. 13 miles - the initial 10 miles = 3 additional miles from his starting point.

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15 Dec 2025, 09:18

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So the cyclist has to go x distance and return the same distance and then travel the 10 miles which it was far from home.
Total distance to be travelled: 10x + 2x

Speed is 3 minutes per mile then in 60 minutes the cyclist will travel 20 miles.

So, (10+2x)/20 = (48/60) Converting 48 minutes to hours.
=> 10 + 2x = 16
we get x = 3

Bunuel

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15 Dec 2025, 09:18

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Bunuel

Speed = 3 mins per mile

To travel 10 miles, the cyclist will need 30 mins.

Hence he they can only travel 18 more minutes, 9 mins to and 9 mins fro.

If the cyclist takes 3 mins to cover 1 mile, in 9 mins, the cyclist can cover 3 miles.

Option B.

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15 Dec 2025, 09:19

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Bunuel

We have,

10 miles from home and C = 3 min./mile
48 minutes to cover extra distance and then ride back home; i.e. 2x + 10 distance in 48 minutres
So 2x + 10 = 16; x =3

Therefore the cyclist can travel an additional 3 minutes before returning home.

Correct option is option B

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15 Dec 2025, 09:19

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48/3= 16 miles
16 - 10 miles= 6miles

6/2= 3miles ( divide by 2 because it is a round trip)

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15 Dec 2025, 09:21

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Let x be extra miles farther from home.

Given: Speed = 3 Min/mile i.e. 1/3 mile/min. & Total Time = 48 min.

Total Distance = Distance out + Distance back =x+10+x=10+2x

=> Total distance = Speed * Time
=> 10+2x=1/3*48 => x=3mile (B)

Therefore, Cyclist can move 3 mile more farther before turning back.

Bunuel

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15 Dec 2025, 09:23

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Speed of the cyclist = 1 miles / 3 minutes = 1/3 miles/minute
Time needed to return back = 10/(1/3) = 30 minutes

Let the additional miles the cyclist can travel away from home = x miles
Time available = 48 - 30 = 18 minutes
Distance to be travelled = 2x miles
Speed = (1/3) miles / minutes

2x = (1/3)*18 = 6
x = 3 miles

The cyclist can travel 3 additional miles

IMO B

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15 Dec 2025, 09:24

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He has total 48 mins to cover the additional distance and return home.

His constant speed is 3mins/mile so for covering the 10mins he need, 10*3 = 30mins

He is left with 18mins in which he can cover 18/3 = 6miles.

Hence he can cover 3 miles additional before turning around (so that he covers remaining 3 miles after he turns around)