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A car travels from city a to city B, a distance of 240kms...

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by swerve » Sun Dec 03, 2017 12:59 pm
A car travels from city a to city B, a distance of 240kms. The car travels half the distance at x kmph and the remaining distance at x+20 kmph. If the car has to complete the journey in less than 5 hours what should be the minimum value of x?

A) 20
B) 30
C) 40
D) 50
E) 60

The OA is C.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
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by [email protected] » Sun Dec 03, 2017 7:17 pm
Hi swerve,

We're told that a car travels a distance of 240 km. The car travels HALF the distance at X km/hr and the remaining distance at (X+20) km/hr. We're asked to find the MINIMUM value of X if the car has to complete the journey in less than 5 hours. This question can be solved by TESTing THE ANSWERS. Since the prompt asks for the MINIMUM value for X, we should start with Answer A. If that doesn't 'fit', we next Test Answer B, and so on. I'm going to do the first set of calculations, then you can finish the work to find the correct answer....
IF.... X = 20
The two speeds are 20 km/hr and 40 km/hr
120 km at 20 km/hr takes 6 hours
120 km at 40 km/hr takes 3 hours
Total time = 9 hours... but this is TOO BIG (it's supposed to be LESS than 5 hours), so Answer A is TOO SLOW.

What happens when you TEST Answer B? Does that 'fit' or do you have to continue working?

Final Answer: C

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Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Fri Jan 12, 2018 6:38 am
swerve wrote:A car travels from city a to city B, a distance of 240kms. The car travels half the distance at x kmph and the remaining distance at x+20 kmph. If the car has to complete the journey in less than 5 hours what should be the minimum value of x?

A) 20
B) 30
C) 40
D) 50
E) 60
We see that the first half of the journey takes 120/x hours and the second half takes 120/(x+20) hours. Assuming that the journey takes exactly 5 hours, we can create the following equation:

120/x + 120/(x+20) = 5

Multiplying the entire by x(x+20) we have:

12(x+20) + 120x = 5x(x+20)

120x + 2400 + 120x = 5x^2 + 100x

5x^2 - 140x - 2400 = 0

x^2 - 28x - 480 = 0

(x - 40)(x + 12) = 0

x = 40 or x = -12

Since x can't be negative, then x = 40, which must be the minimum value of x.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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