time x speed = distance

Question

Yacht and Steamboat: Great! You'll be traveling on the steamboat and the yacht. The steamboat makes the trip in 5 hours. The yacht makes the trip in 2.5 hours. The yacht is 20 knots faster than the steamboat. For each boat, the trip time multiplied by the speed equals the distance traveled. You know both boats will travel the same distance. How fast is each boat traveling in knots (nautical miles per hour)?

Answer 1

For the steamboat:

time = 5

rate = r (because we don't know the rate)

Since distance = rate * time

distance = 5*r

For the yacht

time = 2.5

rate = r+ 20 (because it's 20 knots faster than the steamboat)

Since distance = rate * time

distance = 2.5(r+20)

distance = 2.5r + 50

Since the distance traveled is equal for both the steamboat and the yacht, we can set the distance equations equal to each other

5r = 2.5r + 50

Now we can solve for r, which is the rate of the steamboat. Then we can take that value and solve for the rate of the yacht.