Two window washers start at heights different heights. One is 21 ft. high and riding at a rate of 8 in./s, the other is at 50 ft high and descending a 11 in./s. Write and solve an equation to find how long it takes the two window washers to reach the same height?
Let's first convert the rates of the window washers to the same unit. We will convert the rate of the first window washer from inches per second (in./s) to feet per second (ft/s).
The first window washer is riding at a rate of 8 in./s, which is equivalent to 8/12 = 2/3 ft/s.
The second window washer is descending at a rate of 11 in./s, which is equivalent to 11/12 ft/s.
Now let's denote the time it takes for both window washers to reach the same height as t, measured in seconds.
After t seconds, the first window washer will have traveled a distance of (2/3)t feet, starting from a height of 21 ft.
After t seconds, the second window washer will have traveled a distance of (11/12)t feet, starting from a height of 50 ft.
To find when the two window washers reach the same height, we need to solve the following equation:
21 + (2/3)t = 50 - (11/12)t
Multiplying both sides of the equation by 12 to remove the fractions, we get:
252 + 8t = 600 - 11t
Combining like terms, we have:
19t = 348
Dividing both sides of the equation by 19, we find:
t = 18.32 seconds
Therefore, it will take approximately 18.32 seconds for the two window washers to reach the same height.
To find out when the two window washers will reach the same height, we need to set up an equation based on their respective positions and rates of change.
Let's assume that t represents the time (in seconds) it takes for the window washers to reach the same height.
For the first window washer (ascending), we can use the equation:
Height1 = 21 ft + (8 in./s) * t
For the second window washer (descending), we can use the equation:
Height2 = 50 ft - (11 in./s) * t
To find when the two washers will reach the same height, we set these two equations equal to each other:
21 ft + (8 in./s) * t = 50 ft - (11 in./s) * t
First, we need to convert the units so that they are the same. Let's convert inches to feet by dividing by 12:
21 ft + (8/12 ft/s) * t = 50 ft - (11/12 ft/s) * t
Next, we can simplify the equation by combining terms on each side:
(8/12 ft/s + 11/12 ft/s) * t = 50 ft - 21 ft
(19/12 ft/s) * t = 29 ft
Now we can solve for t by multiplying both sides of the equation by the reciprocal of (19/12 ft/s), which is (12/19 ft/s):
t = (29 ft) * (12/19 ft/s)
t ≈ 18.316 seconds
Therefore, it takes approximately 18.316 seconds for the two window washers to reach the same height.
converting to feet:
21 + (8/12)t = 50 - (11/12)t
solve for t
or
converting to inches:
252 + 8t = 600 - 11t
you will get the same solution for t