a boat leaves the harbor and travels 11 mph toward a small island. 3 hours later, a cabin cruiser leaves the same harbor and travels 33 mph. how many hours after the cabin cruiser leaves the harbor will be next to the motorboat
let the time taken by the cabin cruiser to catch up to the boat be t hours
So 33t = 11(t+3)
33t = 11t + 33
22t = 33
t = 33/22 = 3/2
check:
the boat went for 3+3/2 or 4.5 hours
at 11 mph, went 49.5 miles
the cruiser went for 3/2 hours at
33 mph, went 49.5
looks like it caught up
My answer is correct
so the cabin cruiser caught up in 3/2 hours?
Yes, I think I had that.
Look at my definition of t
To determine how many hours after the cabin cruiser leaves the harbor it will be next to the motorboat, we need to calculate the time it takes for the cabin cruiser to catch up with the motorboat.
Let's denote the time it takes for the cabin cruiser to catch up as 't' hours.
In the 3 hours it takes for the cabin cruiser to leave the harbor, the motorboat has already covered a distance of 3 hours × 11 mph = 33 miles.
Since both boats are traveling towards the island, we can set up an equation using the formula distance = speed × time for both boats.
For the cabin cruiser:
Distance covered by the cabin cruiser = speed of the cabin cruiser × time taken
Distance covered by the cabin cruiser = 33 mph × t hours
For the motorboat:
Distance covered by the motorboat = speed of the motorboat × time taken
Distance covered by the motorboat = 11 mph × (t + 3) hours
Since the distance covered by both boats is the same when the cabin cruiser catches up, we can set up an equation:
33 mph × t hours = 11 mph × (t + 3) hours
Now, we can solve this equation to find the value of 't'.
33t = 11(t + 3)
33t = 11t + 33
33t - 11t = 33
22t = 33
t = 33 / 22
t = 1.5
Therefore, it will take 1.5 hours after the cabin cruiser leaves the harbor for it to be next to the motorboat.