Question

Two ships make the same voyage of 3000 nautical miles. The faster ship travels 10 knots faster than the slower one (a knot is 1 nautical mile per hour). The faster ship makes the voyage in 50 hr less time than the slower one. Find the speeds of the two ships.

Answer 1

Speed of faster ship = f
Speed of slower ship = f-10
Distance = 3000 n.miles
Using distance = speed * time, which means
time = distance/speed
3000/(f-10)-3000/(f) = 50
multiply by f(f-10) on both sides:
3000f-3000(f-10) = 50(f)(f-10)
Expand and simplify:
50*f^2-500*f-30000=0
or
f^2-10*f-600=0
Factorize
(f-30)(f+20)=0
giving f=30 or f=-20. Reject negative solution of f=-20.
We are left with
f=30
The faster ship's speed is 30 knots.
So the slower ship cruises at 20 knots.