12 Days of Christmas GMAT Competition - Day 2: Emma is driving from

Question

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

Emma is driving from home to an appointment at a community center. She travels 40 miles in the first hour but realizes that at this speed, she will arrive 1 hour late. She increases her speed by 20 miles per hour for the remainder of the trip and arrives 20 minutes early. How far is the community center from her home?

A. 140 miles
B. 160 miles 
C. 180 miles
D. 200 miles
E. 220 miles

Bunuel · Accepted Answer

GMAT Club's Official Explanation:

Assume the remaining distance to the community center after the initial 40 miles have been covered is d miles. Then:

• d/40 represents the time it would take to cover the remaining distance if Emma continued driving at 40 mph. 
• d/60 represents the time it would take to cover the remaining distance when she increased her speed to 60 mph (40 + 20).

Since the first time is 1 hour longer than the desired time, and the second time is 1/3 hour shorter (20 minutes) than the desired time, we have:

• d/40 - 1 = d/60 + 1/3
  • d = 160

Therefore, the total distance from Emma's home to the community center is (the initially covered distance) + d = 40 + 160 = 200 miles.

Answer: D.

Krunaal · Answer

Distance = Speed * Time

If Emma travels at 40mph she'll be 1 hour late =>  40*(t+1) = d  ..................where t = total time and d = total distance

For remainder of the trip i.e. d - 40, she increases her speed by 20mph, and arrives 20 minutes (1/3 hr) early =>  60*(t-1-1/3) = d-40

60*(t-4/3) + 40 = 40*(t+1)
t=4
 d=200

Answer D.

Nutella024 · Answer

There are two methods
Method 1 : Forcing the answers
For the 40 miles speed was 40Mph (40/1) and post that the speed was 40+20 = 60. Also, we know that the difference in time between first and second speeds is -> 1 hour plus 20 min -> 1:20
Now Start from option 
A) 140 - 40 we get 40 hours, for 40 Mph the time is 2:30, and for 60, the time is 1:40 not the answer
b) 160 - 40 = 120. For 40 Mph, the time is 3 Hours, and for 60 Mph, it is 2 hours. This is not the answer, but we are getting close.
c) 180 - 40 = 140 for 40 MPH the time is 3:30 and for 60 the time is 2:20, so close
D) 200 - 40 = 160, for 40 MPH the time is 4 hours, and for 60 the time is 2:40 hence, 4-2:40 we get 1:20, the answer

hr1212 · Answer

Let time taken be 't' when speed is increased from 40 miles/hr to 60 miles/hr, which means

Total distance travelled = 40 * 1 + 60 * t --- (1)

Time taken to travel at 40 miles/hr is 1 hr more than the expected time which is 1/3 (20 mins) more than time t + 1, which means the time taken while travelling at 40 miles/hr is (t + 1 + 1 + 1/3) = t + 7/3.

So, total distance travelled at 40 miles/hr = 40 * (t + 7/3) --- (2)

Equating (1) and (2)

40 + 60t = 40(t + 7/3)
t = 8/3

Substituting value in (2)

d = 40 (8/3 + 7/3) = 40 * 5 = 200

Answer : D

ashminipoddar10 · Answer

initial speed= 40 miles/h
initial time taken= 1 hr more than ideal time
Hence we can infer that the total distance is a multiple of 40. By that logic we are only left with B and D

so if d=160 miles

then time taken with 40 miles/h = 4 hours
ideal time= 3 hours
with 60 miles/h after the 1st hour, time taken= 120/60=2 hours
In this case Emma reaches at the exact time and not 20 mins earlier

if d=200 miles
time taken with 40miles/h= 5 hours
ideal time = 4 hours
Time taken to cover the remaining distance after 1st hour= 160/60= 2 hour 40 mins
Hence total time taken= 3 hour 40 mins, i.e. 20 mins earlier,

Hence (D) is the answer

twinkle2311 · Answer

Let the total distance to the community center be D miles.

At 40 mph, she is 1 hour late. At increased speed (60 mph), she arrives 20 minutes early.

The time saved by increasing speed is 1 + 1/3 = 4/3 hours. This time is saved over the remaining D - 40 miles.

Time saved equation: Time difference between speeds: (D - 40)/40 - (D - 40)/60 = 4/3.

Simplify:
--> 3(D - 40) - 2(D - 40) / 120 = 4/3. 
--> (D - 40)/120 = 4/3
--> D - 40 = 160
--> D = 200.

Final answer: 200 miles (D)

siddhantvarma · Answer

Let d: distance between home and community center
For the first 40 miles covered in 1 hour, speed = 40 miles/hour
Let t: time she needs to reach the community center by
Covering a distance of d in 40 miles/hour she'll be 1 hour late => 40 = d/t+1 ....................... (1)

Now she decides to speed up by 20 miles per hour for the remaining (d-40 miles) of the trip
Speed = 60 miles/hour
She arrives 20 minutes or 1/3 hours early in this case
Actual time: t-1 (she already covered first 40 miles in 1 hour)
Time for arriving early= t-1-1/3
60 = d-40/(t-1-1/3) ...................... (2)

Eliminate variable t from equations (1) and (2) and solve for d.
We can substitute t = d/40 - 1 from (1) into (2):

60 = (d-40)/(t-4/3)
t-4/3 = (d-40)/60
d/40 - 1 - 4/3 = (d-40)/60
d/40 - 7/3 = (d-40)/60

Multiplying both sides by 60;
6/4d -140 = d-40
3/2d - d = 140-40 => 1/2d = 100 => d = 200

Therefore community center is 200 miles from her home =>  D. 200 miles

aviraj1703 · Answer

Total distance = d miles
Actual time required = t hours

1) When Emma reaches 1 hour late.
Throughout the speed is 40miles/hour.
d = 40*(t + 1) ...(i)

2) When Emma reaches 20mins(1/3 hours) early.
d = d1 + d2
d = 40 + 60*(t - 1 - 1/3)
put value of (i)
t = 4

put this is in (i)

d = 200 miles.

AviNFC · Answer

Let actual time taken is t+1 hr. In both the cases, the person travelled for 1hr at 40 km/h.
The difference is in the rest of journey.
Case1: distance = 40*t
case2: distance = 60*(t-4/3)

40t = 60t -80
t=4

total distance=(40*4)+40 = 200 miles

Ans D

Purnank · Answer

Emma's Home <-------------------------(D) Distance --------------------------> CC
Lets say with usual speed s she reaches Community Center in t hrs.

as per given condition when speed is at 40 mph she will get delayed by 1 hr.
Therefore Distance  = D = 40 (t+1)

and now if she increases speed by 20 mph for rest of the journey she will arrive 20 min early (1/3 of Hr)

Therefore Same distance  = D = 40 + 60*(t - 1 - \frac{1}{3})

Equating both and solving,

40 (t+1) = 40 + 60*(t - 1 - \frac{1}{3})

Dividing by 20,

2t + 2 = 2 + 3(t - 1 - \frac{1}{3})

2t = 3t - 3 - 1

t = 4 Hr

Therefore, Distance between her home and community center is D = 40(t+1) = 40*5 = 200 miles.

Answer is D.

HarshaBujji · Answer

Let's say t is expected time. So distance travelled if she continues with 40mph

40(t+1). This distance is now covered in 60mph. time is t-1/3 hr.

40(t+1) = 60(t-1/3) 
=> 40t+40 = 60t -20. 
t=3;

So distance is 160 + 40(1st hr) = 200m. 
 
IMO D

bellsprout24 · Answer

Answer is  D. 200 miles

Hour 1 = 40mph and Hours 2+ = 60mph
200 miles at 40mph = 5 hours of driving total, but she will be 1 hour late, so she only has 4 hours available
200 - 40 = 160 miles at 60mph = 2 hours and 40 minutes + 1 hour at 40mph = 3 hours and 40 minutes of driving total after increasing her speed

If she is 1 hour late from 5 hours of driving, and 20 minutes early from 3 hours and 40 minutes of driving, then her available time for driving is 4 hours, and both expressions are in agreement.

missionmba2025 · Answer

Let's assume that the distance from Emma's house to appointment center is 'd'

Distance travelled in the first hour = 40 miles

Remaining Distance = d - 40

\frac{d - 40 }{ 40} + 1 = t + 1

\frac{d - 40 }{ 40} = t

When Emma increases her speed

\frac{d - 40 }{ 60} + 1 = t - \frac{1}{3}

\frac{d - 40 }{ 60} + 1 = \frac{d - 40 }{ 40} - \frac{1}{3}

Taking 120 as LCM on RHS and LHS

2d - 80 + 120 = 3d - 120 - 40

d = 240 - 80 + 40 = 200

Option D

rns2812 · Answer

Assume distance between home to community centre = D 
Expected Time to reach there on time = T

First 1 hr : 
Distance covered = 40 miles 
Speed = 40 miles/hour 
Time taken = 1 hr

Also given at this speed she will be 1 hr late

T + 1 =  \frac{D}{40 }  --- (1)

Rest of the journey 
Distance covered = D - 40 
Speed = Previous speed + 20 miles/hr = 40 + 20 = 60 miles/hr 
Time taken =  \frac{(D-40)}{60 }

Total time taken = 1 +  \frac{(D-40)}{60 }    = T -  \frac{20}{60}  --- (2)

Substituting for T from (1) in (2) and solving

D = 200 miles (OPTION D)

dtxgmat · Answer

OPTION D

Assuming x as the distance, t as the target time

Statement 1: 
After spending the 1st hour (driving 40 miles), she would reach an hour late if she continued at the same speed

= 1 +  \frac{x-40}{40}  = t +1

= t =  \frac{x-40}{40}

Statement 2: 
After 1 hour she sped up to 60 miles/hour and reaches 20 minutes early which is 1/3rd of an hour

Time spend to cover the remaining distance (x - 40 miles) at the new speed =  \frac{x-40}{60} 
New time (converting 20 mins into hours) = t -  \frac{20}{60}

= 1 +  \frac{x-40}{60}  = t -  \frac{1}{3}

= replace equation from statement 1

= 1 +  \frac{x-40}{60}  =  \frac{x-40}{40}  -  \frac{1}{3}

= 4/3 = (x - 40) * (  \frac{1}{40}  -  \frac{1}{60} )

= 160= x - 40

= x = 200

OPTION D

mpp01 · Answer

For solving this question I would split the journey in two parts:
1. We know that she traveled at 40mph for 1 hour = 40 miles traveled + If she kept driving at 40mph she would arrive 1 hour late.
 
 Denote "x" remaining part of the journey 
 T as time of arrival 
 (40 + x )/40 = T

2. Second part of the question exposes she increases speed up to 60mph for the remaining part of the trip "x miles" and finally arrives 20min earlier.
 
 20min = 1/3 of an hour 
 40miles/40mph = 1 hour 
 xmiles/60mph second part of the trip 
 40miles/40mph + xmiles/60mph = T - 1h -1/3h 
 As we calculated T = (40 + x)/40 and substituting 
 1 + X/60 = (40+X)/40 -1 -1/3 
 1 + X/60 = 40/40 + X/40 -1 -1/3 
 1 + X/60 = X/40 -1/3 
 X/60 - X/40 = -4/3 
 -X/120 = -4/3 
 X = 160 miles

But most importantly you must add 40 miles to that distance to answer the question correclty, thus 160 + 40miles = 200miles

Lizaza · Answer

Let's say that t is the time left before Emma's appointment. 
 Then, the distance  S = 40(t+1) = 40*1 + 60(t-1-0.33) , which we get from the task as follows: she would arrive 1 hour later had she continued at 40 mph; and she eventually covered the distance by going 1h at 40mph and some remaining time minus 20 mins (0.33h) going at 40+20=60)

So,  40t + 40 = 40 + 60t - 60*1.33  
  20t = 60*1.33  
  t = 3*1.33 = 4(h)

Then insert this into the original equation: 
  S = 40(t+1) = 40(4+1) = 200

So,    the answer is D.

Divyanshu14 · Answer

KarishmaB

Is there any quick method that can be applied here?

Bunuel · Answer

Not every question has a quick shortcut. However, this thread includes  many  different solution approaches, so I suggest going through them carefully and taking time to understand each. If it's still unclear, feel free to ask a specific question.

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