Problema Solution
john runs at an average rate of 5 mph, while lucy runs at an average rate of 3.5 mph. if lucy starts running at 10.00am, and john begins running the same track at 10.30am, at what time will john catch up with lucy
Answer provided by our tutors
let
v1 = 5 mph average speed of John
v2 = 3.5 mph average speed of Lucy
t1 = the time in hours that John runs until he catches up on Lucy
t2 = the time in hours that Lucy runs until John catches up
d = the distance they both pass before they meet
since Lucy starts running at 10.00am, and John begins running the same track at 10.30am that is 30 min = 0.5 hours later
t2 = t1 + 0.5
the average rate = the distance passed/the total time that is v = d/t = > d = v*t
d = v1*t1 = v2*t2
5*t1 = 3.5*t2
by solving the system of equations
t2 = t1 + 0.5
5*t1 = 3.5*t2
we find
t1 = 7/6 hours = 1 1/6 hours = 1 hour 60/6 min = 1 hour 10 min
t2 = 5/3 hours = 1 2/3 hours = 1 hour 2*60/3 min = 1 hour 40 min
10.30am + 1 hour 10 min = 11.40am
John will catch up with Lucy at 11.40am.