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# Tim and Élan are 90 miles away from one another. They are starting to

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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05 Jun 2016, 21:46
2
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00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:29) correct 33% (02:15) wrong based on 156 sessions

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Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?

(A) 30 miles.
(B) 35 miles.
(C) 45 miles.
(D) 60 miles.
(E) 65 miles.

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Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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16 Jun 2017, 05:00
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Bunuel wrote:
Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?

(A) 30 miles.
(B) 35 miles.
(C) 45 miles.
(D) 60 miles.
(E) 65 miles.

The ratio of speeds of Tim and Elan is 2:1. When their speed doubles, the ratio still remains 2:1 since the speed of both doubles.
So, in the same time, whatever distance is between them, they will cover it in the ratio 2:1.
Since distance between them is 90 miles, which is equivalent to 3 on the ratio scale, it gives us the multiplier 30.
The actual distance covered by Tim is 2*30 = 60 miles.

For more on this, check: https://www.veritasprep.com/blog/2011/0 ... os-in-tsd/
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Manager
Joined: 29 Nov 2011
Posts: 91
Re: Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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05 Jun 2016, 22:04
1
2
total distance between them is 90
first hour
5+10 = 15 distance is covered
second hour
10+20= 30 distance is covered
third hour
20+40= 60 but remaining is 45 to be covered so calculate time here
60 miles in 1 hour
45 miles in -- 45/60 = 3/4 hour
T speed is 40 this time so ... distance covered by him is 3/4*40 = 30
total dis by T is 10+20+30= 60
Manager
Joined: 18 Jan 2010
Posts: 245
Re: Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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05 Jun 2016, 22:19
1
Bunuel wrote:
Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?

(A) 30 miles.
(B) 35 miles.
(C) 45 miles.
(D) 60 miles.
(E) 65 miles.

In 1st hour: Relative speed of the two will be 10+5 = 15 miles / hour. As they move towards each other, The distance between them reduces by 15 miles. Distance left between them: 90 - 15 = 75 miles.

In 2nd hour: Speed of Tim: 20Mph, That of Elan: 10 Mph. Relative speed of the two will be 20+ 10 = 30 miles / hour. As they move towards each other, The distance between them reduces by 30 miles. Distance left between them: 75 - 30 = 45 miles.

In 3rd hour: Speed of Tim: 40 Mph, That of Elan: 20 Mph. Relative speed of the two will be 40+ 20 = 60 miles / hour.

Now in order to cover the remaining distance of 45 miles. They will take: (45/ 60) hrs. = (3/4) hour.

Distance travelled by Tim?

In first hour: 1 hour * (10 miles per hour) = 10 miles
In second hour: 1 hour * (20 miles per hour) = 20 miles
In third hour: (3/4) hour * (40 miles per hour) = 30 miles

Total distance travelled: 10+20+30 = 60 miles.

Director
Joined: 20 Feb 2015
Posts: 756
Concentration: Strategy, General Management
Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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06 Jun 2016, 03:15
Since they are travelling towards each other the speed needs to abe added !!

Distance = 90 miles
first hour !!
total distance travelled = 10+5=15 miles
distance left = 90-15 =75 miles
second hour !!
total distance travelled = 20+10=30 miles (speed doubles)
distance left = 75-30=45 miles
third hour !!
total distance travelled = 40+20=60 miles
since distance left is only 45 miles
time taken to complete 45 miles = 45/60 = 3/4 hour
in this period , distance travelled by tim = (3/4)*40=30 miles
Total distance travelled by tim = 10 + 20 + 30 = 60 miles
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GPA: 2.81
Re: Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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06 Jun 2016, 05:24
2
Bunuel wrote:
Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?

(A) 30 miles.
(B) 35 miles.
(C) 45 miles.
(D) 60 miles.
(E) 65 miles.

Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.

Plugging in the answer choice Only Answer Choice D meet the 2:1(Tim:Elan=60:30) ratio of maintaining total distance traveled 90 miles

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Joined: 15 Jan 2017
Posts: 340
Re: Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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02 Aug 2017, 01:28
I solved it with this logic. A little visually though:
------>Tim: 10,20,40,80,160 (we consider only upto 80 as beyond that no point doubling speed)
80,40,20 ,10,5 <-------
we see the overlap in terms of 40 mph and 20 mph
20 we can discard Elan would be too far even if he doubled his speed, 80 would mean Tim overshot Elan
with regard to 40, we do 90/40 --> 9/4. If we divide 90 into 4 parts we get approx 25/25/25/25 (les than 100 though). 9/4 ~ 3/2 which is then 3 parts out 2; approximately 60 (it has to be more than 45 but less than 65)
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Joined: 27 Oct 2016
Posts: 14
Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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02 Aug 2017, 03:50
Tim's disatnce after 3.5 hrs is 60 miles
Elan's distance after 3.5 hrs is 30 miles.

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Re: Tim and Élan are 90 miles away from one another. They are starting to  [#permalink]

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05 Mar 2019, 10:09
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Re: Tim and Élan are 90 miles away from one another. They are starting to   [#permalink] 05 Mar 2019, 10:09
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