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A bus from city M is traveling to city N at a constant speed

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A bus from city M is traveling to city N at a constant speed [#permalink] New post 10 Jul 2019, 11:26
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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
[Reveal] Spoiler: OA

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Re: A bus from city M is traveling to city N at a constant speed [#permalink] New post 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


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
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Re: A bus from city M is traveling to city N at a constant speed [#permalink] New post 11 Jul 2019, 05:11
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This was good :)
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Re: A bus from city M is traveling to city N at a constant speed [#permalink] New post 11 Jul 2019, 07:14
GreenlightTestPrep wrote:
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


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



Very tough :cry:
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Re: A bus from city M is traveling to city N at a constant speed [#permalink] New post 11 Jul 2019, 08:09
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AlaminMolla wrote:

Very tough :cry:


Very tough indeed! A 165+ level question for sure.

Cheers,
Brent
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Re: A bus from city M is traveling to city N at a constant speed   [#permalink] 11 Jul 2019, 08:09
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A bus from city M is traveling to city N at a constant speed

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