A boat has a speed of 15 mph in still water. It travels downstream from Greentown to Glenavon in g hours. It then goes back upst
ream from Glenavon to Cambria, which is 2 miles downstream from Greentown, in g hours. Find the rate of the current.
1 answer:
Step-by-step explanation:
We want to find two things-- the speed of the boat in still water and the speed of the current. Each of these things will be represented by a different variable:
B = speed of the boat in still water
C = speed of the current
Since we have two variables, we will need to find a system of two equations to solve.
How do we find the two equations we need?
Rate problems are based on the relationship Distance = (Rate)(Time).
Fill in the chart with your data (chart attached)
The resulting speed of the boat (traveling upstream) is B-C miles per hour. On the other hand, if the boat is traveling downstream, the current will be pushing the boat faster, and the boat's speed will increase by C miles per hour. The resulting speed of the boat (traveling downstream) is B+C miles per hour. Put this info in the second column in the chart. Now plug it into a formula! <u>Distance=(Rate)(Time) </u>Now solve using the systems of equations!
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I don't know for sure, but I think there might be an error in the way you copied your function. In all of my dealings with these types of problems, I have learned the formula to be h(t) = 15 + 10t - 16t^2. Notice the plus in front of the "10t". This is due to the fact that if he pushes off of the overhang he would have an upward force of 10 feet per second as soon as his feet left the ground. The only thing pulling him back to Earth is gravity, modeled by the "-16t^2". This is derived from a bit of slightly advanced physics involving the gravitational constant, but let's work under my formula for a second...
Either way, we will wind up using the Quadratic Formula (or possibly factoring if the numbers are easy enough to work with). So let's start.
h(t)= 15 +10t - 16t^2
In order to use the QF or factoring I will need to make h(t)=0. Simply done by:
0= 15 +10t -16t^2
Looking at the numbers, I'd prefer to use the QF so here it is:
I know that my answer will need to be positive since you can't have a negative value when dealing with time, so I will eliminate the positive sign from the "+or-" part leaving me with:
And I know that a= -16, b= 10, and c=15. So all that's left to do is substitute and solve.
There's a decent amount of math that would be difficult and sloppy for me to do over the computer, but all you need to do is solve the rest of the equation and you would get your answer.
Exact answer:
or rounded answer: ≈1.31 seconds.
Hope this helps!
NoThisIsPatrick
Either way, we will wind up using the Quadratic Formula (or possibly factoring if the numbers are easy enough to work with). So let's start.
h(t)= 15 +10t - 16t^2
In order to use the QF or factoring I will need to make h(t)=0. Simply done by:
0= 15 +10t -16t^2
Looking at the numbers, I'd prefer to use the QF so here it is:
I know that my answer will need to be positive since you can't have a negative value when dealing with time, so I will eliminate the positive sign from the "+or-" part leaving me with:
And I know that a= -16, b= 10, and c=15. So all that's left to do is substitute and solve.
There's a decent amount of math that would be difficult and sloppy for me to do over the computer, but all you need to do is solve the rest of the equation and you would get your answer.
Exact answer:
Hope this helps!
NoThisIsPatrick