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Answer:
<em>Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour</em>
Step-by-step explanation:
<u>Relative Speed</u>
When a body is moving at a constant speed v, the distance traveled in a time t is:
When Roberto rows downstream, his speed in still water is added to the speed of the water, making it easier to travel the required distance.
When Roberto rows upstream, his speed in still water is affected by the speed of the water, both are subtracted and the required distance is covered in more time.
Let's call
x = Roberto's rowing speed in still water
y = Speed of the river current
The speed when rowing downstream is x+y, thus the distance traveled is
Where t1=2.5 hours. Substituting values:
Rearranging, we find the downstream equation:
The speed when rowing upstream is x-y, and the distance traveled is
Where t2=5 hours. Substituting values:
Rearranging, we find the upstream equation:
Multiplying [1] by 2:
Adding this equation to [2]:
Solving:
Dividing [2] by 5:
Solving for y
Thus, Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour
Answer: 2405970 ways
Step-by-step explanation:
When the order of selecting r individuals out of n individual , we use permutations.
The number of permutations of r things taking out of n things is given by :-
Given : There are 135 people and three door prizes .
i.e. n= 135 , r= 3
Then, the total number of ways =
Hence, there are 2405970 ways to distribute door prizes of $7,500, $750 and $75 .