Question

On Tuesday and Wednesday of last week I left home for school at the same time. On Tuesday I drove 40 mph (miles per hour) on my way to school and arrived 3 minutes late. On Wednesday I drove 50 mph on my way to school and arrived 2 minutes early. How far do I live from work?

Answer 1

16.67 miles

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