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Rahim plans to drive from city A to station C, at the speed of 70 km

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Bunuel
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Rahim plans to drive from city A to station C, at the speed of 70 km [#permalink] New post   08 Jan 2020, 02:33
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Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southeast of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

(A) 6:15 am
(B) 6:30 am
(C) 6:45 am
(D) 7:00 am
(E) 7:15 am


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nick1816
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Re: Rahim plans to drive from city A to station C, at the speed of 70 km [#permalink] New post   08 Jan 2020, 08:06
C should be in the Southwest Of A

BCA is a (60-90-30) triangle. hence, BC= 500/2=250 Km and AC= 500*\((\frac{\sqrt{3}}{2})\)

Time taken by train to reach C= 250/50= 5hr
Train will arrive C at 1 PM

hence, Rahim must arrive C latest by 12:45 PM

Time taken by Rahim to reach C= \(\frac{250\sqrt{3}}{70} \)= 6.18 hrs =~ 6 hrs 12 mins

The latest time by which Rahim must leave A and still catch the train= 1245 - 612 =~ 0633 hrs or 6:33 AM

B


Bunuel wrote:
Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southeast of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

(A) 6:15 am
(B) 6:30 am
(C) 6:45 am
(D) 7:00 am
(E) 7:15 am


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exc4libur
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Rahim plans to drive from city A to station C, at the speed of 70 km [#permalink] New post   29 Jan 2020, 08:13
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Bunuel wrote:
Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southeast of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

(A) 6:15 am
(B) 6:30 am
(C) 6:45 am
(D) 7:00 am
(E) 7:15 am


C is located at:
{A}N…
W{C}E
…S{B}

Angles: CAB=30, ABC=60, ACB=90
Distance: AB=500 is opposite angle ACB=90
Specials: 30:60:90=x:x√3:2x=250:250√3:500
AB=500, AC=250√3, CB=250
Train at B departs 08:00 and arrives 250/50=5hrs at 13:00
Rahim's takes 250√3/70=~250*7/4/70=6:15hrs from A to C
Rahim's latest: 13:00-15min-6:15hrs=13-6.5=6.5=06:30hrs

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lstudentd
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Re: Rahim plans to drive from city A to station C, at the speed of 70 km [#permalink] New post   22 Nov 2020, 21:01
Bunuel VeritasKarishma Is there an official solution to this with a diagram? I tried drawing it out but couldn't reconcile all the points with the directions provided. Primarily, how can B be south of A, if C is located between west and northwest of B and between south and southeast of A?
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Re: Rahim plans to drive from city A to station C, at the speed of 70 km [#permalink] New post   23 Nov 2020, 11:18
Bunuel can you explain with a diagram? I am not able to understand the location of three stations relative to each other
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Rahim plans to drive from city A to station C, at the speed of 70 km [#permalink] New post   20 Feb 2021, 01:37
jcuh wrote:
Bunuel can you explain with a diagram? I am not able to understand the location of three stations relative to each other


Hi jcuh

See attached the different locations of cities A, B and C. My triangle is not drawn to scale, just focus on the angles to understand the associated distances between any 2 cities.

I hope it helps,
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Cities A,B,C.jpg
Cities A,B,C.jpg [ 523.35 KiB | Viewed 11676 times ]

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Rahim plans to drive from city A to station C, at the speed of 70 km [#permalink]
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