Problema Solution
Id Dr Shukie rides his bike to his office, he averages 12 miles per hour. If he drives his car, he averages 36 miles per hour. His time driving is 1/4 hour less than his time bicycling. How far is his office? (in Miles)
Answer provided by our tutors
let
d = the distance to the office
v1 = 12 miles/h
v2 = 36 miles/h
t1 = the bicycling time
t2 = the driving time
we use the formula average speed = total distance / total time that is
v = d/t, where v=speed, d=distance, t=time
d = v*t
time driving is 1/4 hour less than his time bicycling
t2 = t1 - 1/4
v1*t1 = d = v2*t2
12*t1 = 36*t2
by solving the system of equations
t2 = t1 - 1/4
12*t1 = 36*t2
we find
t1 = 0.375 hours
t2 = 0.125 hours
d = v1*t1 = 12*0.375 = 4.5 miles
the distance to the office is 4.5 miles.