Problema Solution
At 6:00 pm joe begins walking from home to a nearby park to play. His walking speed is 3 miles per hour. At 6:09 pm his sister begins riding her bike from to the park. Her riding speed is 12 miles per hour. She catches up with joe just as he gets to the park. How far in miles is the park from home?
Answer provided by our tutors
let
d = the distance from Joe's home to the park
v1 = 3 mph the walking speed of Joe
v2 = 12 mph the riding speed of Joe's sister
t1 = the walking time of Joe
t2 = the riding time of his sister
the distance that Joe walks is
d = t1*v1
3*t1 = d
the distance that his sister rides is
d = t2*v2
12*t2 = d
since he starts walking at 6:00 and his sister starts riding at 6:09 that is 9 minutes or 9/60 hours later we can write
t2 = t1 - 9/60
we have the follwoing system of equations
3*t1 = d
12*(t1 - 9/60) = d
by solving it we find
t1 = 02 hours
d = 0.6 miles
The park is 0.6 miles from Joe's home.