Problema Solution
Ivan and Kate live 40 miles apart. If Ivan started pedaling towards Kate at 8:00 a.m. at a steady 12 mph while Kate left to meet Ivan at 9:30 a.m. but rode at 16 mph, at what time will they meet?
Answer provided by our tutors
Let
d = 40 mi the distance between Ivan and Kate
v1 = 12 mph the rate of Ivan
v2 = 16 mph the rate of Kate
t = the time of Kate
t + 1.5 = the time of Ivan (since the difference in time between 8:00 am and 9:30 am is 1 hour and 30 min or 1.5 hours)
We know that speed = distance/time follows distance = speed*time:
v1*(t + 1.5) + v2*t = d
12(t + 1.5) + 16t = 40
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t = 11/14 hr
t = 11*60/14 min
t = 47 min
47 min after 8:00 am is 8:47 am
Ivan and Kate will meet at 8:47 am.