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 be the speed (mph) of boat 1. The spead of boat 2 is x+4. Now then, regardless of the relative speeds, the sum of the two boats travel is 9.8 miles. They travel this distance in .7 hours or 9.8/.7= 14 mph.
So, you have x + (x+4) = 14 or:
2x+4=14 or 2x=10 or x=5
To set up this problem, we will use the formula: Distance = Speed * Time.
Let's assume that the speed of the smaller sailboat is 'x' miles per hour. According to the problem, the larger sailboat sails 4 miles per hour faster than the smaller boat, so the speed of the larger sailboat is 'x + 4' miles per hour.
Now, let's calculate the distance each boat travels in 0.7 hours.
For the smaller sailboat:
Distance = Speed * Time
Distance = x * 0.7
Distance = 0.7x
For the larger sailboat:
Distance = Speed * Time
Distance = (x + 4) * 0.7
Distance = 0.7x + 2.8
Since the two sailboats are 9.8 miles apart and sailing toward each other, the sum of their distances will be equal to the distance between them:
0.7x + 0.7x + 2.8 = 9.8
Now, solve for 'x'.
Combine like terms:
1.4x + 2.8 = 9.8
Subtract 2.8 from both sides:
1.4x = 7
Divide both sides by 1.4:
x = 5
So, the speed of the smaller sailboat is 5 miles per hour.
To find the speed of the larger sailboat, substitute 'x' back into the equation:
Speed of the larger sailboat = x + 4 = 5 + 4 = 9 miles per hour.
Therefore, the speed of the smaller sailboat is 5 miles per hour, and the speed of the larger sailboat is 9 miles per hour.