Problema Solution
Darren drives to school in rush hour traffic and averages 20 mph. He returns home in mid-afternoon when there is less traffic and averages 50 mph. WHat is the distance between his home and school if the total traveling time is 1 hr 45 min?
Answer provided by our tutors
let
v1 = 20 mph the avg. rate to school
t1 = the time of the ride to school
v2 = 50 mph the avg.rate from school to home
t1 = the time of the ride home
d = distance
since speed = distance/time => distance = time*speed
d = t1*v1 = t2*v2
20t1 = 50t2
the total traveling time is 1 hr 45 min = 1 45/60 hr = 1.75 hr
t1 + t2 = 1.75
by solving the system of equations
20t1 = 50t2
t1 + t2 = 1.75
we find
t1 = 1.25 hr
t2 = 0.5 hr
click here to see the step by step solution of the system of equations
d = 1.25*20
d = 25 mi
the distance between school and home is 25 miles.