Can someone please help me understand ?
Mathematics

Tutor: None Selected  Time limit: 1 Day 
Two friends enjoy competing with each other to see who has the best time in running a mile. Initially (before they ever raced each other), the first friend runs a mile in 7 minutes, and for each race that they run, his time decreases by 11 seconds. Initially, the second friend runs a mile in 7 minutes and 17 seconds, and for each race that they run, his time decreases by 15 seconds. Which will be the first race in which the second friend beats the first?
race numberThank you for the opportunity to help you with your question!
First, recall that 1 minute = 60 seconds, so 7 minutes is actually 7 * 60 = 420 seconds.
Next, represent the time for each runner on the nth race. Let T(1,n) be the time for the 1st friend on the nth race.
Let T(2,n) be the time for the 2nd friend on the nth race. We want to find the smallest value of n for which
T(2,n) > T(1,2).
According to the problem statement T(1,n) = 420  11*n and T(2,n) = 420 + 17  15*n.
If T(2,n) > T(1,n) then 437 15n > 420  11n. Now subtract 420 from both sides of the inequality, getting
17 15n > 11n. Next, add 15n to both sides, getting 17 > 4n, Next, divide both sides by 4, getting n < 17/4.
Now 17/4 < 16/4 = 4, so n must be equal to 4.
Check T(1,4) = 420  44 = 376 and T(2,4) = 437  60 = 377 so (as expected) T(1,4) < T(2,4).
Secure Information
Content will be erased after question is completed.