two brothers walk toward each other from a starting distance of 1200 meters. the elder walks at 80 meters per minute while the younger walks at 70 meters per minute. how long does it take them to...

two brothers walk toward each other from a starting distance of 1200 meters. the elder walks at 80 meters per minute while the younger walks at 70 meters per minute. how long does it take them to be only 450 meters from each other for the first time?

Expert Answers
electreto05 eNotes educator| Certified Educator

The distance traveled by each brother in a time t, is equal to its speed by time:

d = vt

So we can say that:

The oldest brother travels, in time t, a distance d1 = v1 t

The younger brother travels, in time t, a distance d2 = v2 t

The total distance can be expressed as follows:

d = d1 + d2 + 450

1200 = v1 t + v2 t + 450

1200 = t(v1 + v2) + 450

Solving for the time t:

t = (1200 - 450)/(80 + 70)

t = 5 minutes

So, they have walked for 5 minutes before being only 450 m from each other.