Problema Solution
A speedboat takes 2 hour longer to go 35 miles up a river than to return. If the rate of the current is 1 mile per hour, what is the rate of the boat?
Answer provided by our tutors
Let x miles/hour be the speed of the boat. Then according to the question :
Then going up the river, the speed of the boat is (x-1) miles/hour.
Going down the river, the speed is (x+1) miles/hour. As per the speed distance time formula, (distance/speed) = time.
=> 35/(x-1) - 35/(x+1) = 2
=> 35(x+1) - 35(x-1) = 2 (x-1)(x+1)
=> 35x + 35 - 35x + 35 = 2x2 - 2
=> 2x2 - 2 - 70 = 0
=> x2 = 36
=> x = 6
Therefore the speed of the boat is 6 miles/hour.