Rate and Distance

[BTGmoderatorRO]

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
oa is b.

I am confused on how to set up the formulas here. Can any experts help?

[GMATGuruNY]

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

Anne:
Traveling for 4 hours at a speed of 25 mph, the distance traveled = rt = 25*4 = 100 miles.
Traveling for 4 hours at a speed of 45 mph, the distance traveled = rt = 45*4 = 180 miles.
Since Anne's speed was between 25 mph and 45 mph, the distance from A to B must be BETWEEN 100 AND 180 MILES.
Eliminate A and E, which are not between 100 and 180.

John:
Traveling for 2 hours at a speed of 45 mph, the distance traveled = rt = 45*2 = 90 miles.
Traveling for 2 hours at a speed of 60 mph, the distance traveled = rt = 60*2 = 120 miles.
Since John's speed was between 45 mph and 60 mph, the distance from A to B must be BETWEEN 90 AND 120 MILES.
Eliminate C and D, which are not between 90 and 120.

The correct answer is B.

[Scott@TargetTestPrep]

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
oa is b.

I am confused on how to set up the formulas here. Can any experts help?

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