Anne traveled from City A to City B in 4 hours, and her speed was betw

Question

Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95
B. 115
C. 125
D. 160
E. 180

Kudos for a correct solution.

A. 95 
B. 115 
C. 125 
D. 160 
E. 180

PS04808

shailendra79s · Accepted Answer

For Anne:
Minimum Distance possible = Minimum Speed x Time = 25*4 = 100 miles
Maximum Distance Possible = Max. Speed x Time = 45*4 = 180 miles

For John:
Minimum Distance possible = Minimum Speed x Time = 45*2 = 90 miles
Maximum Distance Possible = Max. Speed x Time = 60*2 = 120 miles

The range for distance traveled by John & Anne between A & B is from 100 to 120 miles
Only Answer (B) - 115 Miles is in between the range.

mejia401 · Answer

A is out since the minimum cannot be below 100. 
C,D,E are out because the maximum for the second car is 120.

Thus, B.

Kr,
Mejia

ENGRTOMBA2018 · Answer

Distance range per Anne's speed : 25*4 - 4*45 ---> 100 - 180 ...(1)

Distance range per John's speed : 45*2 - 60*2 ----> 90-120 ....(2)

(2) eliminates C,D,E and (1) eliminates A.

B is the correct answer.

KS15 · Answer

Using the given options,
A.95. If distance=95 miles, and Anne takes 4 hours, then her speed=95/4=23.xx(Her speed is b/w 25 and 45 miles per hour) . So this is out
B 115. If distance=115 miles, and Anne takes 4 hours, then her speed=115/4=28.75 miles per hours(looks good) and John takes 2 hours.His speed=115/2=57.5 miles per hours(looks good)

Answer B

VenoMfTw · Answer

IMO : B Given 25 < S_a < 45 45 < S_b < 60 T_a = 4 T_b = 2 Distance is same for both S_a T_a = S_b T_b S_a * 4 = S_b * 2 2* S_a = S_b Thus from the above equation the condition is restricted to as follows 25 < S_a < 30 50 < S_b < 60 As if S_a > 30 then S_b must be >60 which is not possible Thus sub in Distance = S_b * T_b Distance = 2 * S_b Thus Distance varies from 100 < Distance < 120 Thus from the options only 115 satisfies this condition

holybanker · Answer

Time spent by John is half the time than the time spent by Anne, as the speed of Anne is beteween the 25-45 range, John could only make the distance at a speed range from 50 to 60, if we multiply this by 2, the range of distances are from 100 to 120, so the only answer compliant with that is B

CounterSniper · Answer

The minimum possible distance = 4*25=100 that eliminates option A
The maximum possible Distance =2*60=120 which eliminates C , D and E
thus we are then left with : B

Lorenzo3688 · Answer

the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95 
B. 115 
C. 125 
D. 160 
E. 180

Distance range per Anne's speed : 25*4 - 4*45 ---> 100 - 180 ...(1)

Distance range per John's speed : 45*2 - 60*2 ----> 90-120 ....(2)

(2) eliminates C,D,E and (1) eliminates A.

B is the correct answer.

TheMechanic · Answer

Excellent question.

Quick Question: How do I add this question on my downloadable PDF file???

ENGRTOMBA2018 · Answer

Click on "Add question to pdf question list" as marked in the attached image. 1-28-16 2-16-14 PM.jpg

ScottTargetTestPrep · Answer

Let’s use the minimum and maximum speeds.

Minimum for Anne: 25 x 4 = 100 miles

Maximum for Anne: 45 x 4 = 180 miles

Thus:

100 < d < 180

Minimum for John: 45 x 2 = 90 miles

Maximum for John: 60 x 2 = 120 miles

Thus:

90 < d < 120

Using both inequalities, we have:

100 < d < 120

Answer: B

Giro2345 · Answer

Bunuel   ScottTargetTestPrep

Quick question:

Is there a general rule for combining inequalities?

While working on this question, i simply added the inequalities (because the signs of the inequalities face the same direction).

By doing this, i got the result:

100 < d < 180
90 < d < 120
----------------- =
190 < 2d < 300

divide by 2

95 < d < 150 .

This approach leaves the answers options b and c.

Did i proceede correct?

Or is there a different rule for combining the inequalities?

Thank you in advance!

ScottTargetTestPrep · Answer

No, you can’t add double inequalities when the variable is the same. If they are different variables, then yes.

For example, if A < x < B and C < y < D, then A + C< x + y < B + D.

However, if A < x < B and C < x < D, then we can’t add them. The correct inequality for the latter case is max(A, C) < x < min(B, D).

For example, if 3 < x < 10 and 5 < x < 12, then 5 < x < 10.

Notice that we did not actually add together these inequalities to come up with 5 < x < 10.

energetics · Answer

25 < Anne rate < 45 * 4 hr = d
45 < John's rate < 60 * 2 hr = d

Test the answers:
C) 125/4 = 31.25, OK for Anne. 125/2 = 62.5, too high for John
Go lower because C was too high
B) 115/4 = 28.75, OK for Anne. 115/2 = 57.5, OK for John. 
B is the answer.

DanTheGMATMan · Answer

Have to go with the most restrictive range to satisfy both travelers:

https://www.youtube.com/watch?v=yhBtadztV8g

bumpbot · Answer

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Anne traveled from City A to City B in 4 hours, and her speed was betw

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