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?
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.