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Pascal has 96 miles remaining to complete his cycling trip.

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by BTGmoderatorDC » Sun Jul 28, 2019 8:45 pm
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Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

OA B

Source: Manhattan Prep
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by Jay@ManhattanReview » Mon Jul 29, 2019 9:55 pm
BTGmoderatorDC wrote:Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

OA B

Source: Manhattan Prep
Say Pascal's current speed is x miles per hour

As per the first condition, his speed = (x – 4) mph. Thus, he would take 96/(x – 4) hours to complete the remaining trip.

As per the second condition, his speed = x + 50% of 3x/2 mph. Thus, he would take 96/(3x/2) = 64/x hours to complete the remaining trip.

Given that 96/(x – 4) – 64/x = 16 => x = 8 mph

The correct answer: B

Hope this helps!

-Jay
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by swerve » Tue Jul 30, 2019 10:29 am
We can try as follows:

Let the current speed be \(x\) miles per hour.
Time taken if speed is 50% faster (i.e. \(3x/2 = 1.5x\)) \(= 96/1.5x\)
Time taken if speed is reduced by 4 miles/hr (i.e. \((x-4)\))\( = 96/(x-4)\)

As per question, \(\frac{96}{(x-4)} - \frac{96}{1.5x} = 16\)

Solving this we get \(x = 8\).

So, the correct answer is __B__
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by Scott@TargetTestPrep » Tue Aug 06, 2019 4:47 pm
BTGmoderatorDC wrote:Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

OA B

Source: Manhattan Prep
If we let Pascal’s current rate = r, then his time to complete the remainder of the trip = 96/r.

If we let Pascal’s reduced rate = r - 4, then his new time is 96/(r - 4).

If we let Pascal’s increased rate = 1.5r, then his new time is 96/1.5r = 960/15r = 64/r,

Since the remainder of the trip would take him 16 hours longer with his reduced rate than with his increased rate:

64/r = 96/(r - 4) - 16

Multiplying the entire equation by r(r - 4), we have:

64(r - 4) = 96r - 16r(r - 4)

64r - 256 = 96r - 16r^2 + 64r

16r^2 - 96r - 256 = 0

r^2 - 6r - 16 = 0

(r - 8)(r + 2) = 0

r = 8 or r = -2

Since the rate can’t be negative, r = 8. Pascal’s current rate is 8 miles per hour.

Answer: B

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