Question

HELP!!
How to set this up?
you comment 56 miles one way to work. The trip to work takes 10mins linger than the trip home. YOu average speed on the trip home is 8 miles faster. what is your average speed on the trip home?

Answer 1

Comute (not comment) 56 miles one way.
Rate * time = distance
sounds useful
we know a 1-way trip distance is 56, we we know

rate * time= 56

Let's call the rate to work S (for speed) in miles per hour
and the time T (in hours)

Answer 2

with the definitions

rate to work S (for speed) in miles per hour
and the time T (in hours)

you get the equation S*T=56 (going to work)

now we need an equation for going home.
trip to work takes 10mins longer than the trip home
and hopefully it is clear the trip home takes 10 minutes less than when going to work.

*careful about units* T is in hours. We must change 10 minutes to fractions of 1 hour. 10 min/60 min/hour = 1/6 hour

the time to get back home is T - 1/6

Answer 3

average speed on the trip home is 8 miles faster.

so going home you go (S+8) miles per hour

that means your second equation is
(S+8) (T-1/6) = 56

Answer 4

average speed on the trip home? is going to be S+8 (speed going home)

you have two equations and two unknowns so you can solve for S (and T)
and then S+8

Answer 5

Thanks so much!!