2)A motorboat leaves a dock and travels at an average speed of 15mi/h toward an island. The average speed on the return trip is 10mi/h. How far is the island from the harbor if the total trip takes 5h? (HInt-first find the 2 times)
Let the distance be d miles.
so time towards the island = D/15 hrs
time on return trip is D/10 hrs
isn't D/15 + D/10 = 5 ?
can you solve for D ?
sorry i forgot to put that it took the whole trip 5hr
No, you didn't forget to put that in
I used it in my equation.
So, what did you get?
is it 5 hr
To solve this problem, we need to find the time it takes for the motorboat to reach the island and the time it takes for the motorboat to return to the dock.
Let's represent the distance between the dock and the island as "d" miles.
Let's start with the time it takes for the motorboat to reach the island. We know that the average speed of the motorboat is 15 mi/h, and the total trip takes 5 hours. Let's assume it takes "t" hours for the motorboat to reach the island.
Distance = Speed × Time
d = 15t
Next, let's find the time it takes for the motorboat to return to the dock. We know that the average speed on the return trip is 10 mi/h. Since the total trip takes 5 hours, and the time it took to reach the island is "t", the time it takes to return can be represented as (5 - t) hours.
Now, let's use the formula Distance = Speed × Time again for the return trip.
d = 10(5 - t)
Now we have two equations:
d = 15t
d = 10(5 - t)
Since both equations are equal to "d", we can set them equal to each other:
15t = 10(5 - t)
Simplify the equation:
15t = 50 - 10t
Combine like terms:
25t = 50
Divide both sides by 25:
t = 2
Now that we know it takes 2 hours for the motorboat to reach the island, we can use this value to find the distance:
d = 15t
d = 15(2)
d = 30
Therefore, the island is 30 miles away from the harbor.