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Jeff drives three times farther

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by jack0997 » Wed Jul 19, 2017 12:53 am
Jeff drives three times farther in 36 minutes than what Amy drives in 30 minutes. If Jeff drives at a speed of 40 miles per hour, at what speed, in miles per hour, does Amy drive?

(A) 6
(B) 9
(C) 16
(D) 24
(E) 32

OA C
Pl. help me out to solve this question.
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by GMATGuruNY » Wed Jul 19, 2017 1:06 am
jack0997 wrote:Jeff drives three times farther in 36 minutes than what Amy drives in 30 minutes. If Jeff drives at a speed of 40 miles per hour, at what speed, in miles per hour, does Amy drive?

(A) 6
(B) 9
(C) 16
(D) 24
(E) 32
Jeff drives three times farther in 36 minutes than what Amy drives in 30 minutes.
To determine the ratio of Jeff's speed to Amy's speed, plug in easy values.
Let Amy's speed = 1 mile per 30 minutes.
Since Jeff drives three times farther in 36 minutes, Jeff's speed = 3 miles per 36 minutes.
Convert the two speeds to miles per hour:
Amy = 1 mile per 30 minutes = 2 miles per 60 minutes = 2 miles per hour.
Jeff = 3 miles per 36 minutes = 1 mile per 12 minutes = 5 miles per 60 minutes = 5 miles per hour.

The values in blue imply that Mary's speed is 2/5 of Jeff's speed.
Since Jeff's actual speed = 40mph, we get:
Mary's actual speed = (2/5)(40) = 16mph.

The correct answer is C.
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by Jay@ManhattanReview » Wed Jul 19, 2017 1:37 am
jack0997 wrote:Jeff drives three times farther in 36 minutes than what Amy drives in 30 minutes. If Jeff drives at a speed of 40 miles per hour, at what speed, in miles per hour, does Amy drive?

(A) 6
(B) 9
(C) 16
(D) 24
(E) 32

OA C
Pl. help me out to solve this question.
Jeff's speed = 40 miles per hour

Thus, the distance covered by Jeff in 60 minutes = 40 miles

Thus, the distance covered by Jeff in 36 minutes = (40/60)*36 = ƒ24 miles

This distance of 24 miles is 3 times of what Amy drives in 30 minutes

Thus, distance covered by Amy in 30 minutes = 24/3 = 8 miles

Thus, distance covered by Amy in 60 minutes = (8/30)*60 = 16 miles.

Thus, Amy's speed = 16 miles per hour.

The correct answer: C

Hope this helps!

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by DavidG@VeritasPrep » Wed Jul 19, 2017 7:14 am
jack0997 wrote:Jeff drives three times farther in 36 minutes than what Amy drives in 30 minutes. If Jeff drives at a speed of 40 miles per hour, at what speed, in miles per hour, does Amy drive?

(A) 6
(B) 9
(C) 16
(D) 24
(E) 32

OA C
Pl. help me out to solve this question.
We can also use a little logic and the answer choices. Say Jeff drove three times farther than Amy did in the same interval. He'd have gone three times as fast, right? In this case Amy's speed would have been 40/3 = 13 1/3. But the time interval isn't exactly the same - he goes 3 times as fast in 36 minutes as she goes in 30 minutes, so she'd be going a touch faster than 13 1/3. The only answer that makes sense is C.
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by [email protected] » Wed Jul 19, 2017 8:22 am
Hi jack0997,

The answer choices to this question are sufficiently "spaced out" that we can use estimation, a bit of logic and the answer choices to get to the correct answer.

We're told that Jeff travels 3 TIMES farther in 36 minutes what Amy drives in 30 minutes. Since Jeff takes a bit more time than Amy to travel 3 times her distance, we know that if they traveled the SAME amount of time, then Jeff would travel between 2-3 times Amy's distance.

We're told that Jeff drives 40 miles/hour; we're asked for Amy's speed.

Looking at the answers, let's compare the given value with the 'range' that would be 2-3 times that value.

Answer A: 6 mph --> range = 12mph - 18mph
Answer B: 9 mph --> range = 18mph - 27mph
Answer C: 16 mph --> range = 32mph - 48mph
Answer D: 24 mph --> range = 48mph - 72mph
Answer E: 32 mph --> range = 64mph - 96mph

Jeff's speed is 40mph - and that value falls into just ONE of the ranges above, so that range MUST be the answer.

Final Answer: C

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by Matt@VeritasPrep » Sun Jul 23, 2017 5:30 pm
D = RT

For Jeff, D = 40 * (3/5 of an hour) = 24 miles

For Amy, D = R * (1/2 of an hour). We know Amy's D = 8, since it's 1/3 of Jeff's D.

That leaves 8 = R * 1/2, or R = 16.
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by Matt@VeritasPrep » Sun Jul 23, 2017 5:32 pm
We could also say that Amy drives (1/3) of Jeff's D in (5/6) of the time, so Amy would drive Jeff's D in 3 * (5/6), or 15/6, or 5/2 of the time.

Since Rate and Time are reciprocal, if Amy's T = (5/2) of Jeff's, then Amy's R = (2/5) of Jeff's. (2/5) of 40 is 16, and we're done.
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by Jeff@TargetTestPrep » Tue Jul 25, 2017 11:11 am
jack0997 wrote:Jeff drives three times farther in 36 minutes than what Amy drives in 30 minutes. If Jeff drives at a speed of 40 miles per hour, at what speed, in miles per hour, does Amy drive?

(A) 6
(B) 9
(C) 16
(D) 24
(E) 32
We can first calculate the distance Jeff drives in 36 minutes (notice that 36 min. = 36/60 = 3/5 hour):

Distance = rate x time

Distance = 40 x 3/5

Distance = 24 miles

Since this distance is 3 times as far as Amy drives in 30 minutes, Amy drives 24/3 = 8 miles in 30 minutes, which means she drives 16 miles in 60 minutes, or 16 miles in an hour.

Answer: C

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