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# My friend sets out walking at a speed of 3 miles per hour. I set out behind her 5 minutes later at 4 miles per hour. For how many minutes wi

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My friend sets out walking at a speed of 3 miles per hour. I set out behind her 5 minutes later at 4 miles per hour. For how many minutes will my friend have been walking when I catch up to her? Please help!

Jan 27, 2019

$$\text{suppose your friend sets out at time }t=0\\ \text{her distance from wherever she they started from is }3t\\ \text{similarly your distance from the same spot is }\\ 4\left(t - \dfrac{4}{60}\right)\\ \text{you meet your friend when these two are equal}\\ 3t = 4\left(t - \dfrac{4}{60}\right)\\ \dfrac{16}{60}=\dfrac{4}{15}=t\\ t = \dfrac{4}{15}~hr = 16~min$$