Problema Solution
A cruise ship can sail 28 mph in calm water. Sailing with the Gulf Stream, the ship can sail 170 mi in the same amount of time as it takes to sail 110 mi against the Gulf Stream. Find the rate of the Gulf Stream.
Answer provided by our tutors
(Vs + Vg) * t = 170 mi
(Vs - Vg) * t = 110 mi
First solve for the time (t) by eliminating Vg, adding those two equations:
2 * Vs * t = 280 mi
Vs * t = 140 mi
t = (140 mi) / (28 mph) = 5 hr
Now just plug that time (t) into either of the other equations. I suggest BOTH, as a sanity check to ensure you got it right:
(Vg * 5hr) + (28 * 5 mi) = 170 mi
Vg * 5hr = 30 mi
Vg = 6mph
Now the equation for going AGAINST the stream, just to be safe:
( -Vg * 5hr ) + (28 * 5 mi) = 110 mi
( -Vg * 5hr ) = -30 mi
- Vg = -6mph
Vg = 6mph