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If Teena is driving at 55 miles per hour and is currently 7.5 miles be

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If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Joe?

A. 15
B. 60
C. 75
D. 90
E. 105
[Reveal] Spoiler: OA

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If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 04 Jan 2016, 21:30
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Bunuel wrote:
If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Joe?

A. 15
B. 60
C. 75
D. 90
E. 105


This question tests your concepts of relative speed and distance

Teena is 7.5 miles behind joe and needs to get 15 miles ahead of Joe.
Hence Teena needs to cover a total of 22.5 miles with respect to Joe.

The relative speed of Teena with respect to Joe = 55 - 50 = 15 miles/hour

Hence Teena will be able to cover this distance in 22.5/15 hours = 90 Minutes

Option D
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Last edited by OptimusPrepJanielle on 29 Aug 2017, 06:13, edited 1 time in total.

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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 06 Jan 2016, 02:42
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Total distance teena has to drive = 7.5 + 15 =22.5 miles
relative speed =55-40=15 miles per hour
time taken by her to reach 15 miles ahead of joe = 22.5/15=3/2=1.5 hours =90 minutes

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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 01 Feb 2016, 16:18
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This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.

Teena covers 55 miles in 60 mins.
Joe covers 40 miles in 60 mins

So teena gains 15 miles every 60 mins

Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins

So answer 30+60= 90 mins.

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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 02 Apr 2017, 12:16
Super shortcut
Time =initial separation/Relative speed
=7.5/(55-40)
=7.5/15
=1/2 HRS OR 30 MIN
NOW 7.5 miles....30 min
15 miles.....60 min
Total time (30+60)=90 min

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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 02 Apr 2017, 12:55
Bunuel wrote:
If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Joe?

A. 15
B. 60
C. 75
D. 90
E. 105


let h=hours for T to get 15 miles ahead of J
h(55-40 mph)=7.5+15 miles
h=1.5 hours=90 minutes
D

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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 25 Jun 2017, 15:09

It is a good idea to first establish catch up or shrink rate after one unit of time



Tina is catching up to Joe at 15 mph.
In 1 hour she would have passed Joe and gone ahead by 7.5 miles. Hence to reach 15 miles ahead of Joe, she needs half an hour more.

Answer is 1.5 hrs or 90 minutes, D
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If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 26 Jun 2017, 05:05
If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Joe?

Speed (Teena) = \(55 \frac{Miles}{Hour}\)

Speed (Joe) = \(40 \frac{Miles}{Hour}\)

Distance Between Teena and JOe = 7.5 Miles, Total Distance Teena has to cover = 7.15 + 15 = 22.5 Miles

As both Teena and Joe are moving in the same direction, we have to substract the higher speed from the lower speed to get the relative speed

= \(55 \frac{Miles}{Hour}\) - \(40 \frac{Miles}{Hour}\) = \(15 \frac{Miles}{Hour}\)

So, lets calculate the time required for Teena to cover 22.5 miles

\(Time = \frac{Distance}{Speed}\)

\(= \frac{22.5}{15}\)

= 1.5 Hrs

As the time asked in the question is in minutes we will multiply it by 60

\(= 1.5 * 60\)

\(= 90 Min\)


Hence, the Answer is D
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If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 22 Aug 2017, 18:12
JeffTargetTestPrep - Could you please explain this question in line with your explanation here. Thanks in advance.

Here is what I did as per your approach:

S(Teena) = 55
D = x+7.5
T = t

S(Joe) = 40
D = x
T = t

x+7.5 =55t --- (1)
x = 40t --- (2)

Therefore, t = 1/2 (OR) 30 mins, which is when they will both be caught up. Total distance scaled by them is x = 20 miles

Now, to the remaining part of the question, where it says Teena is 15 miles ahead of Joe - which translates to:

D = 20 + 15 +7.5 = 42.5 miles
T = t
S = 55 mph

T = 42.5/55*60 (because they wanted the time in minutes) ~ 46 minutes. Where am I going wrong?

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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 22 Aug 2017, 19:31
Joe is driving at 40 mph, Teena at 55 mph. So in one hour teena will gain 15 miles over joe (55-40). Teena starts at -7.5 miles wrt joe. and we need to find when teena is +15 miles wrt joe. So basically she has traveled an equivalent of 90 min (60 min for 15 miles and 30 min for 7.5 miles) to reach 15 miles ahead of joe.
Hence answer is D!
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New post 22 Aug 2017, 22:41
Blackbox wrote:
JeffTargetTestPrep - Could you please explain this question in line with your explanation here. Thanks in advance.

Here is what I did as per your approach:

S(Teena) = 55
D = x+7.5
T = t

S(Joe) = 40
D = x
T = t

x+7.5 =55t --- (1)
x = 40t --- (2)

Therefore, t = 1/2 (OR) 30 mins, which is when they will both be caught up. Total distance scaled by them is x = 20 miles

Now, to the remaining part of the question, where it says Teena is 15 miles ahead of Joe - which translates to:

D = 20 + 15 +7.5 = 42.5 miles
T = t
S = 55 mph

T = 42.5/55*60 (because they wanted the time in minutes) ~ 46 minutes. Where am I going wrong?


Hi Blackbox,

Please find highlighted portion.
In the time that Teena catches up with Joe,
she travels about 20 + 7.5 miles that she was away.
Therefore, Teena travels a distance of 27.5 and not 20.

Now that both of them are at the same point, we need to use the relative speed
Relative speed at which Teena is moving ahead is 55-40 or 15mph(as they are travelling in the same direction)
and it will take her an hour(60 minutes) to overtake Joe by 15 miles.

Since, we have been asked to find the total time, it would be 30+60(90) minutes

Hope that helps you!
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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be [#permalink]

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New post 23 Aug 2017, 20:20
Thank you, pushpitkc.

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Re: If Teena is driving at 55 miles per hour and is currently 7.5 miles be   [#permalink] 23 Aug 2017, 20:20
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