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At 3:00 pm, a car has driven 30 miles east. It will continue to drive

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At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

a) 10
b) 11
c) 12
d) 13
e) 14


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[Reveal] Spoiler: OA

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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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0.8 minutes --> 1 mile
1 minute --> 1/0.8 = 10/8 = 1.25 miles/minute

Distance covered in 40 minutes = 1.25 * 40 = 12.5 * 4 = 50 miles

Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
30 + x = 50 - x
2x = 20
x = 10

Answer: A

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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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snorkeler wrote:
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

a)10
b)11
c)12
d)13
e)14


Source: Prep4GMAT


Find the speed of the car from "at 0.8 minutes per mile".
In 60 mins, it will drive (1/0.8) * 60 = 75 miles

In 40 mins (2/3 hr), the car can drive 75 * (2/3) = 50 miles.

It needs to cover the 30 miles back to the original point from here so from here, it has only 50 - 30 = 20 miles left to go forward and return.
This means it can go 10 miles forward and return back here.

Answer (A)
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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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New post 02 Jun 2016, 22:28
snorkeler wrote:
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

a)10
b)11
c)12
d)13
e)14


Source: Prep4GMAT


the car travels for 40 minutes @0.8 minutes per mile..
so it travels \(\frac{40}{0.8} = 50\)miles in 40 minutes..

these 50 miles include 30 miles that he has to cover one side...
so distance till he turns around =\(\frac{50-30}{2} = 10\)
A
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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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snorkeler wrote:
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

a)10
b)11
c)12
d)13
e)14


Source: Prep4GMAT



At 3 pm a car is 30 miles east from its starting point. Now after travelling some distance x, let us say the car turns back. Now this car covers x+30 miles to reach starting point.

Now when this car reaches starting point the time is 3:40 PM.

This means that in 40 minutes, this car has travelled a distance of x +x + 30 Miles.

x miles the car is travelling further East

x+30 This car has turned and is travelling in opposite direction, i.e. West.


Total distance: 2x+30 miles.

Speed of car is given in convoluted form. 8 minutes per mile.

0.8 minute -------car covers ----------1 mile
In 1 minute ---this car will cover---- 1/0.8 mile = 1.25 miles.

Speed of car: 1.25 miles per minute

so \(\frac{2x+30}{1.25}\) = 40 minutes

2x+30 = 50

2x = 20.

x = 10 miles.
Answer: A

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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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snorkeler wrote:
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?
a)10
b)11
c)12
d)13
e)14
Source: Prep4GMAT

Distance covered by Car in .8 mins = 1 mile
distance covered by car in 1 min = 1/(.8) = 1/(4/5) = 5/4 = 1.25 mile

Car continues to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point .
Time needed by car to cover 30 miles that was driven before 3 pm = 30/(5/4) = 24 mins

Since car needs to arrive back to its original starting point by 3:40 pm , we have 16 mins of travel time left . This time needs to divided equally in travel time in opposite directions .
So , the car will travel 8 mins towards east and 8 mins towards west .

Distance car can drive before turning around = (5/4) * 8 = 10 miles
Answer A
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At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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New post 30 Jun 2016, 05:56
adiagr wrote:
snorkeler wrote:
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

a)10
b)11
c)12
d)13
e)14


Source: Prep4GMAT



At 3 pm a car is 30 miles east from its starting point. Now after travelling some distance x, let us say the car turns back. Now this car covers x+30 miles to reach starting point.

Now when this car reaches starting point the time is 3:40 PM.

This means that in 40 minutes, this car has travelled a distance of x +x + 30 Miles.

x miles the car is travelling further East

x+30 This car has turned and is travelling in opposite direction, i.e. West.


Total distance: 2x+30 miles.

Speed of car is given in convoluted form. 8 minutes per mile.

0.8 minute -------car covers ----------1 mile
In 1 minute ---this car will cover---- 1/0.8 mile = 1.25 miles.

Speed of car: 1.25 miles per minute

so \(\frac{2x+30}{1.25}\) = 40 minutes

2x+30 = 50

2x = 20.

x = 10 miles.
Answer: A



Quote:
Should not this be:
At 3 pm a car is 30 miles East from its starting point.

Now after traveling some distance x (towards East), let us say the car turns back.

Now this car covers X+30 miles (towards West) to reach starting point.

Now when this car reaches starting point the time is 3:40 PM.

This means that in 40 minutes, this car has traveled a distance of x +x + 30 Miles.

Should this NOT be 2 (X+30) Miles ???

Btw, the question says:
How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

That means, car travels for 30 miles and then x miles and then takes a turn.
So, one-way drive would be (30+x) miles, then take a turn, and drive back again (30+x) miles to turn to the starting point.
Is my understanding correct?

Please correct my understanding. A pictorial representation would help me understand. Somehow, I am stuck at this concept.
Thanks a ton!

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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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yosita18 wrote:
adiagr wrote:
snorkeler wrote:
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

a)10
b)11
c)12
d)13
e)14


Source: Prep4GMAT



At 3 pm a car is 30 miles east from its starting point. Now after travelling some distance x, let us say the car turns back. Now this car covers x+30 miles to reach starting point.

Now when this car reaches starting point the time is 3:40 PM.

This means that in 40 minutes, this car has travelled a distance of x +x + 30 Miles.

x miles the car is travelling further East

x+30 This car has turned and is travelling in opposite direction, i.e. West.


Total distance: 2x+30 miles.

Speed of car is given in convoluted form. 8 minutes per mile.

0.8 minute -------car covers ----------1 mile
In 1 minute ---this car will cover---- 1/0.8 mile = 1.25 miles.

Speed of car: 1.25 miles per minute

so \(\frac{2x+30}{1.25}\) = 40 minutes

2x+30 = 50

2x = 20.

x = 10 miles.
Answer: A



Quote:
Should not this be:
At 3 pm a car is 30 miles East from its starting point.

Now after traveling some distance x (towards East), let us say the car turns back.

Now this car covers X+30 miles (towards West) to reach starting point.

Now when this car reaches starting point the time is 3:40 PM.

This means that in 40 minutes, this car has traveled a distance of x +x + 30 Miles.

Should this NOT be 2 (X+30) Miles ???

Btw, the question says:
How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

That means, car travels for 30 miles and then x miles and then takes a turn.
So, one-way drive would be (30+x) miles, then take a turn, and drive back again (30+x) miles to turn to the starting point.
Is my understanding correct?

Please correct my understanding. A pictorial representation would help me understand. Somehow, I am stuck at this concept.
Thanks a ton!


Responding to a pm:

The question says: "At 3:00 pm, a car has driven 30 miles east."
This means the car has already driven 30 miles east (it uses present perfect tense "has driven" which means the action has just been completed).
It is at a point 30 miles east of its starting point.


S --------------(30 miles) --------------- P (at 3:00)


Now it has to travel further ahead and turn back and reach S by 3:40

S --------------(30 miles) --------------- P (at 3:00)------- (x) -------------->
(at 3:40) <-----------------------------(x + 30)-----------------------------

In 40 mins, it travels x + x + 30 miles.

Does this help?
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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive [#permalink]

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New post 14 Nov 2017, 10:48
snorkeler wrote:
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

a) 10
b) 11
c) 12
d) 13
e) 14


Source: Prep4GMAT

The car has a uniform speed, it travels 1 mile in .8 minutes
so for the last 30 miles it will take 30 * .8 = 24 minutes
So out of a total time of 40 minutes , 24 will be required for the last 30 miles .
So the car has a total 16 minutes to make the forward an return journey.
Which means the car only 8 minutes to travel forward.
we know the speed is 1 mile in .8 minutes , hence in 8 minutes the car will travel 10 miles.

Answer = 10

More elaborately :Let the starting point be S
From point S, a car has traveled 30 miles let this be point B, after which the time is now 3:00 PM, then it has a uniform speed of 1 mile in .8 minutes. The car has to travel forward till say point E then return to point B then continue back 30 miles to point S.

So from B ---E -----B----S the car has a total of 40 minutes . We know the distance from B to S = Distance from S to B hence 30 miles
So time taken for B to S= 24 minutes ( 30 * .8)
Hence only 16 minutes from B to E and E to B , or only 8 minutes one way .
A car taking .8 minutes to travel 1 mile , will travel 10 miles in 8 minutes.
Answer = 10.
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Re: At 3:00 pm, a car has driven 30 miles east. It will continue to drive   [#permalink] 14 Nov 2017, 10:48
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