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!
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
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.