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# My friend... Any help is appreciated!

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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!

Kenzie1778  Sep 17, 2017
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#1
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At 3 mph....your friend covers  3 / 60   miles per minute

At 4 mph......you cover  4/ 60    miles per minute

So....every minute....you close    [  4 - 3 ]/ 60   =  1/ 60   miles  on your friend

And when she has been walking for 5 minutes......she will be  5 * [3  / 60 ]  = 15/60  = 1/4 of a mile ahead of you when you start

So......the number of minutes, m, it will take to catch your friend can be found by :

( 1/60) m  = 1/4      multiply both sides by 60

m =  60  / 4   =    15 minutes

CPhill  Sep 17, 2017
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Let the time taken by your friend =t minutes, then you have:

3t =4(t -5), solve for t

t = 20 minutes taken by your friend

20 - 5 = 15 minutes taken by you.

And this makes sense since you can cover 1 miles in 15 minutes, while it takes her 20 minutes to cover 1 mile.

P.S. The reason that you don't need to divide by 60 is that the ratio of 3:4 remains the same, whether you divide or not.

Guest Sep 17, 2017
edited by Guest  Sep 17, 2017
edited by Guest  Sep 17, 2017

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