Question 455372
Going upstream:
d = rt
r = speed of boat in still water - 3 mph current
d = 35 (given)
35 = (s-3)*t
Going downstream:
d = rt
r = speed of boat in still water + 3 mph current
d = 45 (given)
45 = (s+3)*t
We also are told t is the same for both trips.
But we are not told what t is.
So, we can turn the equations around to be in the form:  t =
Then since t = t, we can solve.
.
35/(s-3) = t
45/(s+3) = t
So,
35/(s-3) = 45/(s+3)
Cross multiply
35*(s+3) = 45*(s-3)
35s + 105 = 45s - 135
Subtract 35s from both sides
105 = 10s -135
Add 135 to both sides
240 = 10s
10s = 240
Divide both sides by 10
s = 24
.
Always check your answers!
In this case, if you plug s=24 into the equations, will the t's be equal?
35/(24-3) = 35/21 = 5/3
45/(24+3) = 45/27 = 5/3
Yes!
.
So the speed of the boat in still water is 24 mph.
.
Done.