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Simple, once you figure it out correctly....
d = rt
Part of the 135 mile trip was taken at 55 MPH and the other part was taken at 40 MPH. So we have two related distance equations to solve.
Let's solve for the 55 MPH part of the trip.
The part of the trip taken at 55 MPH equates to this:
d = 55t
The part of the trip taken at 40 MPH, relative to the other part, looks like this:
135 - d = 40(3 - t)
Add them together: 135 = 55t + 40(3 - t)
Now simplify and solve for t:
135 = 55t + 120 - 40t
135 = 15t + 120
15 = 15t
t = 1
So, the 55 MPH part of the trip took 1 hour so the 40 MPH part took 2 hours. 1 hour at 55 MPH and 2 hours at 40 MPH equal 135 miles.
We can prove it by solving it the other way around.
The part of the trip taken at 40 MPH equates to this:
d = 40t
The part of the trip taken at 55 MPH, relative to the other part, looks like this:
135 - d = 55(3 - t)
Add them together: 135 = 40t + 55(3 - t)
Now simplify and solve for t:
135 = 40t + 165 - 55t
135 = -15t + 165
-30 = -15t
t = 2
So, the 40 MPH part of the trip took 2 hours which matches up perfectly with what we did above.
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