Two sailboats are 9.8 miles apart and sailing toward each other. The larger boat sails 4 miles per hour faster than the smaller boat. The two boats pass each other after 0.7 hour. Find the speed of each boat.
I cannot figure out for the life of me how to set this one up. I already have the answer in the back, but it's just getting this set up is the problem.
Thanks!
Let X = speed of one boat and X + 4 = the other.
.7X + .7(X + 4) = 9.8
I hope this helps. Thanks for asking.
To solve this problem, we can set up a system of equations based on the given information.
Let's denote the speed of the smaller boat as "x" miles per hour. Since the larger boat sails 4 miles per hour faster, its speed is "x + 4" miles per hour.
We know that the distance between the two boats is 9.8 miles and they pass each other after 0.7 hour. The total distance covered by both boats can be calculated as the sum of the distances traveled by each boat.
For the smaller boat, the distance traveled is the product of its speed (x miles per hour) and the time it was sailing (0.7 hour). So, the distance traveled by the smaller boat is 0.7x miles.
Similarly, the distance traveled by the larger boat is the product of its speed (x + 4 miles per hour) and the time it was sailing (0.7 hour). So, the distance traveled by the larger boat is 0.7(x + 4) miles.
Since the total distance covered by both boats is 9.8 miles, we can set up the following equation:
0.7x + 0.7(x + 4) = 9.8
Now, we can solve this equation to find the value of x, which represents the speed of the smaller boat.
0.7x + 0.7x + 2.8 = 9.8
Combining like terms, we get:
1.4x + 2.8 = 9.8
Subtracting 2.8 from both sides, we have:
1.4x = 7
Dividing both sides by 1.4, we get:
x = 5
So, the speed of the smaller boat is 5 miles per hour.
The larger boat's speed is then x + 4 = 5 + 4 = 9 miles per hour.
Therefore, the speed of the smaller boat is 5 miles per hour, and the speed of the larger boat is 9 miles per hour.