M44-03

Question

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

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

Bunuel · Answer

Official Solution:

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

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

Assume the remaining distance to the community center after the initial 40 miles have been covered is  d  miles. Then:
 
•  \frac{d}{40}  represents the time it would take to cover the remaining distance if Emma continued driving at 40 mph.
 
•  \frac{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  \frac{1}{3}  hour shorter (20 minutes) than the desired time, we have:
 
•  \frac{d}{40} - 1 = \frac{d}{60} + \frac{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

bhargavhhhhhhhh · Answer

Hi bunuel, why did we subtract 1 from d/40, we should add right because it will take 1 hour longer similarly to 1/3

Bunuel · Answer

We subtract 1 from d/40 because  d/40  is the time Emma would take  at her current speed  — but the question says this is  1 hour more  than the required time. So:

time taken at 40 mph  =  required time  + 1 hour
 required time  =  d/40 - 1

Similarly, for the faster speed:

time taken at 60 mph  =  required time  - 1/3 hour
 required time  =  d/60 + 1/3

That’s why we subtract 1 and add 1/3 — it depends on what the time  is more or less than .

ledzep10 · Answer

Since the distance traveled by Mary is the same in both scenarios, we can formulate the equations as below:

If the time taken to arrive at the community center is X: T=X

Case 1: The entire journey is travelled at 40mph
D = S x T = 40 (X+1) ; X+1 because it takes an hour longer to reach than the required time

Case 2: The first hour is traveled at 40 mph and the rest of the distance is traveled at 60 mph
D = S x T = 40 x 1 + 60 (X - 1 - 1/3) ; X-1-1/3 because 1 hour has been used in travelling at 40mph and Emma reaches 1/3 hours earlier than the required time to reach.

Equating the two equations since Distance is the same:

40(X+1) = 40 + 60(X-4/3)
40X + 40 = 40 + 60X -80
20X = 80
X = 4

Distance = 40(4+1) = 200

Answer D

agrasan · Answer

Let's say total distance is D and total time required is T

40*(T + 1) = D = 40*1 + (40+20)*(T - 1 - 20min)

20min = 1/3 as time is in hour unit

40*(T + 1) = D = 40*1 + (40+20)*(T - 1 - (1/3))

40*T + 40 = 40 + 60*T - 60*(4/3)

T = 4

D = 40*(T+1) = 40*5 = 200

Dream009 · Answer

See don't get confused. I got confused with the wording what's given is 
Initial speed 40m/ hour at this time required is T+60 mins
New speed - 60 m/hour at this time take is T- 20 mins

S1: S2 = 2:3 this means time ratio is 3k:2k .... for some k 
Now this means T+60 is 3k and T-20 is 2k 
3k-2k = 80 
So actual time taken at 40 m is 80*3 mins = 4* 60 mins = 4 hours. 
So distance is 160m = speed * time
Now don't forget to add 40 to this coz.... all this calculation started from 1 point and that does not includes already travelled 40. Ans is 200

M44-03

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