Problema Solution
Juan drives to work.because of traffic conditions, he averages 22 miles per hour. He returns home averaging 32 miles per hour. The total travel time is 2 1/4 hours.
Define a variable for the time Juan takes to travel to work. Write an expression for the time Juan takes to return home!
write and solve an equation to find the time Juan spends driving to work
Answer provided by our tutors
let
t1 = the time Juan spends driving to work
t2 = the time Juan spend driving back from work
v1 = 22 mph the speed when driving to work
v2 = 32 mph the speed when returning home
t = 2 1/4 = 9/4 = 2.25 hours total travel time
since average speed = distance / travel time we have
v = d/t => t = d/v and d = v*t
we now that the distance back the forth is the same:
v1*t1 = v2*t2
22*t1 = 32*t2
the total time is 2.25 hours
t1 + t2 = 2.25
by solving the system of equations
22*t1 = 32*t2
t1 + t2 = 2.25
we find
t1 = 4/3 hours
t2 = 11/12 hours
we can find the equation for t2 using the system
22*t1 = 32*t2 => t1 = (32*t2)/22
t1 + t2 = 9/4 =>t2 = 9/4 - t1
t2 = 9/4 - (32*t2)/22
t2(1 + 32/22) = 9/4
t2 = 9/4 *(1 + 32/22)^(-1)
Juan spends 4/3 hours to drive to work.