Answer:
16.67 miles
Step-by-step explanation:
We have to:
t = time (in hours) required to arrive on time.
Now the time that is late or earlier, they give it in minutes, therefore it must be spent in hours:
In other words, 3 minutes late is 3/60 hours late, therefore:
t1 = t + 3/60
2 minutes before is 2/60 hours before, therefore:
t2 = t - 2/60
The distance is the same in both directions, so v1 * t1 = v2 * t2
We know that v1 = 40 and v2 = 50 by replacing:
40 * (t + 3/60) = 50 * (t - 2/60)
40 * t + 2 = 50 * t - 5/3
40 * t - 50 * t = -5/3 - 2
-10 * t = -3.66
t = 3.6 / 10
t = 0.366 hours = 0.366 * 60 = 22 minutes
That is, in the first case it takes 25 (22 + 3) minutes, therefore:
40 * 25/60 = 16.66 miles
In the second case it takes 20 (22 -2) minutes, therefore:
50 * 20/60 = 16.66 miles
Therefore lives 16.67 miles from work
