the current in a stream moves at a speed of 10 mph. a boat travels 17 mi upstream and 17 mi downstream in a total time of 10 hr. What is the speed of the boat in still water?
let speed of boat in still water be x mph
17/(x-10) + 17/(x+10) = 10
time (x-10)(x+10)
17(x+10) + 17(x-10) = 10(x^2 - 100)
34x = 10x^2-1000
10x^2 -34x - 1000 = 0
x = 11.84 or some negative speed
x = 11.84
42. A boat can be rowed 9 km. upstream or 18km. downstream in a period of 3 hrs. Whatis the speed of the boat in still water in km/hr? (A) 4 km/hr (B) 45 km/hr (C) 3 km/hr (D) 3-5 km/hr n
To find the speed of the boat in still water, we can use the concept of relative velocity. Let's assume the speed of the boat in still water is 'x' mph and the speed of the stream is 10 mph.
When the boat is moving upstream (against the stream), the speed of the boat relative to the stream is reduced. So, the effective speed of the boat is (x - 10) mph.
When the boat is moving downstream (with the stream), the speed of the boat relative to the stream is increased. So, the effective speed of the boat is (x + 10) mph.
Now, let's calculate the time taken for each leg of the journey:
Time taken to travel upstream = Distance / Speed = 17 miles / (x - 10) mph.
Time taken to travel downstream = Distance / Speed = 17 miles / (x + 10) mph.
According to the problem, the total time taken for the journey is 10 hours:
Time taken upstream + Time taken downstream = 10 hours.
Let's set up the equation and solve for 'x':
17 / (x - 10) + 17 / (x + 10) = 10.
To solve this equation, we can multiply through by the common denominator (x - 10)(x + 10), simplify, and solve the resulting quadratic equation.
17(x + 10) + 17(x - 10) = 10(x - 10)(x + 10).
Simplifying further:
17x + 170 + 17x - 170 = 10(x^2 - 100).
34x = 10x^2 - 1000.
10x^2 - 34x - 1000 = 0.
Now, we can solve this quadratic equation to find the value of 'x' using factoring, completing the square, or the quadratic formula.
Once we have the value of 'x', we can determine the speed of the boat in still water.