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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?

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

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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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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

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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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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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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 _________________

Kudosity killed the cat but your kudos can save it.

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

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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

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 _________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

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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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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!
_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

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