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A bus from city M is traveling to city N at a constant speed
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10 Jul 2019, 11:26
10 Jul 2019, 11:26
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Question Stats:
27% (01:46) correct
72% (03:09) wrong based on 65 sessions
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A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for two hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?
A.48
B.72
C.96
D.120
E. 192
A.48
B.72
C.96
D.120
E. 192
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Re: A bus from city M is traveling to city N at a constant speed
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11 Jul 2019, 04:58
11 Jul 2019, 04:58
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Carcass wrote:
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for two hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?
A.48
B.72
C.96
D.120
E. 192
A.48
B.72
C.96
D.120
E. 192
Buses traveling at SAME speeds meet in point P after driving for 2 hours.
IMPORTANT: Since the 2 buses are traveling at the SAME speed, then point P must be HALF WAY between city M and city N
Also recognize that the TOTAL travel time = 4hrs (2 hrs for each bus)
TOTAL distance traveled = (distance one bus traveled) + (distance other bus traveled)
Distance = (travel time)(rate)
Let r = the rate that EACH bus is traveling.
So, we get: TOTAL distance traveled = 2r + 2r = 4r
So, from the above fact, the distance from point P to city M (and to city N) = 4r/2 = 2r
One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?
Another way to read this is: One bus leaves its city. ONE HOUR LATER, the other bus leaves its city.
Let's say Bus A leaves city M at noon, and Bus B leaves city N at 1pm.
Let t = Bus A's travel time until they meet
So, Let t-1 = Bus B's travel time until they meet
Since the TOTAL travel time = 4hrs, we can write: t + (t-1) = 4
Solve to get: t = 2.5
So, Bus A traveled for 2.5 hours, Bus B traveled for 1.5 hours,
This means Bus A traveled further. In fact, Bus A travels PAST point P (which is halfway between cities M and N) for an ADDITIONAL 24 miles
In other words, Bus A's travel distance = 2r + 24
Since Bus A traveled for 2.5 hours at a rate of r, we can write: 2.5r = 2r + 24
Multiply both sides by 2 to get: 5r = 4r + 48
Solve: r = 48
TOTAL distance traveled = 4r
= 4(48)
= 192
Answer: E
Cheers,
Brent
A bus from city M is traveling to city N at a constant speed
[#permalink]
22 Jan 2022, 03:52
22 Jan 2022, 03:52
3
Carcass wrote:
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for two hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?
A.48
B.72
C.96
D.120
E. 192
A.48
B.72
C.96
D.120
E. 192
Let:
E = the early bus
D = the delayed bus
M = the meeting point on the following day
E and D travel at the same speed.
Implication:
When they travel toward each other, they cover the SAME DISTANCE and thus meet at the HALFWAY POINT.
The following day...one bus is delayed 24 minutes and the other leaves 36 minutes earlier.
Since E leaves 36 minutes early and D 24 minutes late -- yielding a 60-minute difference between their departure times -- E travels on its own for the first hour.
They meet 24 miles from point P.
We can PLUG IN THE ANSWERS, which represent the total distance.
When the correct answer is plugged in, the difference between P and M = 24 miles.
B: 72 miles
On the first day, E and D travel toward each other for 2 hours and meet at the halfway point.
E 0--------->P=36<---------72 D
Since 36 is halfway between 0 and 72, P is at the 36-mile mark.
Since E travels 36 miles eastward in 2 hours, E's rate = d/t = 36/2 = 18 miles per hour.
On the second day, E travels on its own for the first hour at a rate of 18 mph.
Since E travels 18 miles westward, we get:
D 0-----------------54<-----18 miles-----72 E
E is now at the 54-mile mark.
After the first hour, E and D travel toward each other and meet at the halfway point.
Since E and D meet halfway between 0 and 54, we get:
D 0------->M=27<-------54 E
M is at the 27-mile mark.
Difference between P and M = 36-27 = 9
The difference is TOO SMALL.
Eliminate B.
D: 120 miles
On the first day, E and D travel toward each other for 2 hours and meet at the halfway point.
E 0--------->P=60<---------120 D
Since 60 is halfway between 0 and 120, P is at the 60-mile mark.
Since E travels 60 miles eastward in 2 hours, E's rate = d/t = 60/2 = 30 miles per hour.
On the second day, E travels on its own for the first hour at a rate of 30 mph.
Since E travels 30 miles westward in 1 hour, we get:
D 0-----------------90<-----30 miles-----120 E
E is now at the 90-mile mark.
After the first hour, E and D travel toward each other and meet at the halfway point.
Since E and D meet halfway between 0 and 90, we get:
D 0------->M=45<-------90 E
M is at the 45-mile mark.
Difference between P and M = 60-45 = 15
The difference is still TOO SMALL.
Eliminate D.
As the answer choices increase, so does the difference between P and M.
Implication:
For the difference between P and M to reach 24, the correct answer must be GREATER THAN 120.
Show: ::
E
