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# On a 20 km tunnel connecting two cities A and B there are three gutter

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Math Expert
Joined: 02 Sep 2009
Posts: 61544
On a 20 km tunnel connecting two cities A and B there are three gutter  [#permalink]

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09 Jan 2020, 01:21
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29% (03:20) correct 71% (02:41) wrong based on 6 sessions

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On a 20 km tunnel connecting two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from city A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance.

(A) 4 minutes
(B) 2.5 minutes
(C) 1.5 minutes
(D) 1 minute
(E) Patient died before reaching the hospital

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Re: On a 20 km tunnel connecting two cities A and B there are three gutter  [#permalink]

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09 Jan 2020, 02:59
Bunuel wrote:
On a 20 km tunnel connecting two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from city A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance.

(A) 4 minutes
(B) 2.5 minutes
(C) 1.5 minutes
(D) 1.5 minutes
Same Though
(E) Patient died before reaching the hospital

Explanation:

let that the distance of the gutter 1 and A to be x
The gutter 1 and 2 to be y
From the question, we will get that
x+y+2y+x = 20
2x + 3y = 20.
Since we know that the speed x is 30 km/hr and so x = 30*5/60 = 2.5 km ; correspondingly the value of y will be 5km.

Now we know that the ambulance doubles its speed to 60km/hr or we can write 1 km per minute. So the time taken for the remaining journey = 15*2 + 2.5 = 32.5.

Since, it takes 1 min to load and unload the patient so total time will be = 5 + 32.5 + 1 = 38.5 minutes.

So, doctor gets = 40 - 38.5 = 1.5 min to attend the patient.

IMO-C or D
Math Expert
Joined: 02 Sep 2009
Posts: 61544
Re: On a 20 km tunnel connecting two cities A and B there are three gutter  [#permalink]

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09 Jan 2020, 03:01
rajatchopra1994 wrote:
Bunuel wrote:
On a 20 km tunnel connecting two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from city A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance.

(A) 4 minutes
(B) 2.5 minutes
(C) 1.5 minutes
(D) 1.5 minutes
Same Though
(E) Patient died before reaching the hospital

Explanation:

let that the distance of the gutter 1 and A to be x
The gutter 1 and 2 to be y
From the question, we will get that
x+y+2y+x = 20
2x + 3y = 20.
Since we know that the speed x is 30 km/hr and so x = 30*5/60 = 2.5 km ; correspondingly the value of y will be 5km.

Now we know that the ambulance doubles its speed to 60km/hr or we can write 1 km per minute. So the time taken for the remaining journey = 15*2 + 2.5 = 32.5.

Since, it takes 1 min to load and unload the patient so total time will be = 5 + 32.5 + 1 = 38.5 minutes.

So, doctor gets = 40 - 38.5 = 1.5 min to attend the patient.

IMO-C or D

_______________
Fixed. Thank you.
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Re: On a 20 km tunnel connecting two cities A and B there are three gutter  [#permalink]

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10 Jan 2020, 02:16
Re: On a 20 km tunnel connecting two cities A and B there are three gutter   [#permalink] 10 Jan 2020, 02:16
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