Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour?

A. 30 minutes
B. 40 minutes
C. 45 minutes
D. 60 minutes
E. 75 minutes

Since at the time that they stop, the distance they both ran are the same, therefore \(r_{Pam} * t_{Pam} = r_{Cathy} * t_{Cathy}\). Since Pam stopped running for 30 minutes, then \(t_{Cathy}=t_{Pam}+0.5\). Therefore \(10 * t_{Pam} = 8 *( t_{Pam}+0.5)\) yields \(t_{Pam} = 2\). 2 hours or 120 minutes is how long Cathy was running. Since she already ran for 45 minutes, after stretching, she ran for 75 minutes .

This corresponds to E.

Furthermore, \(t_{Cathy}=2+0.5=2.5\) or 150 minutes of total running time. She ran for 45 minutes + 30 minutes, so the difference is again 75 minutes. Corresponding to answer E.

Time to catch up= Distance to catch up / relative speed
Distance to catch up= (8*0.75 - 10*0.75) + 8*0.5 = 2.5 miles
Time to catch up= 2.5/(10-8) = 75 minutes
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Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

\(P = 10\\
C = 8\)

Obtain the distance travelled for both after the break.
\(P \times \frac{3}{4} + 0 \times \frac{1}{2}= \frac{30}{4}\\
C \times (\frac{3}{4} + \frac{1}{2}) = 8 \times \frac{5}{4} = 10\)

Distance difference = \(10 - \frac{30}{4} = \frac{10}{4}\)

Relative speed = \(P - C = 2\)

\(\text{Time for them to meet }= \frac{\text{Distance difference }}{\text{Relative speed}} = \frac{\frac{10}{4}}{2} = \frac{5}{4} = 75 \text{ minutes}\)


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after 75 minutes,
P is (5/4)*8-(3/4)*10=2.5 miles behind C
P gains 10-8=2 mph on C
2.5 miles/2 mph=1.25 hours=75 minutes for P to catch up
E

Hi All,

While this question is a bit 'wordy', solving it simply requires that you stay organized and do the necessary math work step-by-step.

To start, we're given the rates that two women run at and a length of time that they each run for. We can use that data to calculate the distance they both travel...

Pam: runs 10 miles/hour for 45 minutes, then STOPS for 30 minutes = (10 mi/hr)(3/4 hour) = 7.5 miles run
Cathy: runs 8 miles/hour for 1 hour 15 minutes = (8 mi/hr)(5/4 hour) = 40/4 = 10 miles run during that same time

Thus, after 1 hour 15 minutes, Cathy is 2.5 miles AHEAD of Pam

We're then asked how long it will take Pam to 'catch up' to Cathy if Pam runs at 10 miles/hour. Since Pam is now running 2 miles/hour FASTER than Cathy, then Pam will 'catch up' 2 miles every hour. Here, we can take advantage of how the answer choices are written. Cathy is 2.5 miles AHEAD of Pam, so we know that it will take MORE than 1 hour for Pam to catch Cathy. There's only one answer that makes sense...

Final Answer:

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