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John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points.

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John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points.

by Gmat_mission » Sun May 03, 2020 1:26 pm

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John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.

A) 25%
B) 50%
C) 75%
D) 100%
E) 200%

[spoiler]OA=A[/spoiler]

Source: Veritas Prep
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Re: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points.

by deloitte247 » Fri May 08, 2020 5:47 am
Karen is 50% faster than John
So by the time John covers 20% of the total distance, Karen would have covered 20% + (50% of 20%)
= 20% of 10% = 30% and 20 + 30 = 50%

Without John having cramps; for every 50% of the total distance, John will cover 20% and Karen will cover 30%

For the whole (50% * 2 = 100%) John will cover (20% * 2 = 40%) and Karen will cover (30% * 2 = 60%)
But after covering 25% of the total distance, John gets a cramp. So, Karen covered the remaining (100% - 25% = 75%) of the total distance

The percentage increase from what Karen should have covered if John didn't get cramps to what she now has to cover before she can meet with John = $$\left(\frac{new\ dis\tan ce-original\ dis\tan ce}{original\ dis\tan ce}\right)\ \cdot\frac{100}{1}$$
$$\left(\frac{75\%-60\%}{60\%}\right)\ \cdot\frac{100}{1}$$
$$=\frac{15\%}{60\%}\ \cdot\frac{100}{1}$$
$$=0.25\ \cdot\ \frac{100}{1}=25\%$$

Answer = A
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Re: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points.

by Scott@TargetTestPrep » Sat May 09, 2020 5:50 am
Gmat_mission wrote: ↑
Sun May 03, 2020 1:26 pm
 John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.

A) 25%
B) 50%
C) 75%
D) 100%
E) 200%

[spoiler]OA=A[/spoiler]

Source: Veritas Prep
Let’s assume that John runs at 10 mi/hr, and thus, Karen runs at 10 x 1.5 = 15 mi/hour. If we assume that the distance between them was 100 miles, then when John stopped, he had run 25 miles and Karen had to run 75 miles to meet him, and thus her running time was 75 / 15 = 5 hours.

Had John not stopped, they would have met when he had run 40 miles and she had run 60 miles (ratio of 10 : 15); thus, her running time would have been 60 / 15 = 4 hours.

The percent longer that Karen would have had to run is (50 - 40) / 40 x 100% = 25%.

Answer: A

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