A boat's crew rowed 7.5 downstream,with
the current, in 1.5 hours. The return trip upstream against the current,covered the same distance,but took 2.5 hours. Find the crew's rate in still water and the rate of the current.
Rate of still water = 7.5/1.5
Rate of the current water = 7.5/2.5
To find the crew's rate in still water and the rate of the current, we can use the formula:
Speed = Distance / Time
Let's assign variables to the unknown values:
Let "C" be the crew's rate in still water (in miles per hour)
Let "R" be the rate of the current (in miles per hour)
Given:
1. Distance downstream = 7.5 miles
2. Time downstream = 1.5 hours
3. Distance upstream = 7.5 miles (same as downstream)
4. Time upstream = 2.5 hours
Using the formula mentioned earlier, we can set up the following equations:
Equation 1: (C + R) = 7.5 / 1.5
Equation 2: (C - R) = 7.5 / 2.5
Now, let's solve these two equations simultaneously to find the values of C and R.
Multiply both sides of Equation 1 by 1.5:
1.5 * (C + R) = 1.5 * (7.5 / 1.5)
1.5C + 1.5R = 7.5
Multiply both sides of Equation 2 by 2.5:
2.5 * (C - R) = 2.5 * (7.5 / 2.5)
2.5C - 2.5R = 7.5
Now we have a system of equations:
1: 1.5C + 1.5R = 7.5
2: 2.5C - 2.5R = 7.5
We can solve this system using the method of substitution or elimination. Let's use the elimination method.
Multiply Equation 1 by 2.5 and Equation 2 by 1.5 to eliminate the variable "R":
(2.5)(1.5C + 1.5R) = (2.5)(7.5)
(1.5)(2.5C - 2.5R) = (1.5)(7.5)
Simplifying further:
3.75C + 3.75R = 18.75
3.75C - 3.75R = 11.25
Adding both equations together eliminates the "R" terms:
(3.75C + 3.75R) + (3.75C - 3.75R) = 18.75 + 11.25
Simplifying:
7.5C = 30
Finally, divide both sides by 7.5 to isolate "C":
C = 30 / 7.5 = 4
Therefore, the crew's rate in still water is 4 miles per hour.
Now, substitute the value of C into one of the original equations (Equation 1 or 2) to find the value of R.
Using Equation 1:
(4 + R) = 7.5 / 1.5
4 + R = 5
Subtract 4 from both sides:
R = 5 - 4 = 1
Therefore, the rate of the current is 1 mile per hour.
Hence, the crew's rate in still water is 4 mph, and the rate of the current is 1 mph.