5 A boat travels 32 miles up the river in same amount of tim

5) A boat travels 32 miles up the river in same amount of time it takes to travel 44 miles down the same river. If the current is 3 miles per hour, what is speed of the boat in still water?

6) One car travels 280 miles in same amount of time it takes a second car traveling 4 miles per hour slower than the first to go 260 miles. What are the speeds of the cars?

7) A water tank can be filled in 16 hours by an inlet pipe and emptied in 20 hours by an outlet pipe. How long will it take to fill the tank if both pipes are left open?

8) A bathtub can be filled by the cold water faucet in 11 minutes and by the hot water faucet in 14 minutes. How long does it take to fill the tub if both faucets are open?

Solution

5) Let the speed of the boat in still water be x. Then the speed of the boat up the river is x - 3 and the speed down the river is x + 3. Since time =distance/speed,we have 32/(x -3) = 44/(x + 3) or, 32(x +3) = 44(x -3) or, 32x + 96 = 44x -132 or, 44x - 32x = 132+ 96 or, 12x = 228 so that x = 228/12 = 19. Thus, the speed of the boat in still water is 19mph.

6) Let the speed of the first car be x mph. Then the speed of the 2nd car is x- 4 mph. Since time = distance / speed, we have 280/x = 260/(x -4) or, 280(x -4) = 260x or, 280x - 1120 = 26x or, 20x = 1120 so that x = 1120/20 = 56 > Thus, the speed of the two cars are 56mph and 52 mph respectively.

7) The water tank can be filled in 16 hours by an inlet pipe and emptied in 20 hours by an outlet pipe. Therefore, 1/16th of the tank can be filled in 1 hour by the inlet pipe and also, 1/20th of the tank can be emptied in an hour by the outlet pipe. Thus, if both the pipes are left open, in 1 hour , 1/16- 1/20 = 1/80 of the tank will be filled. Therefore, it will take 80 hours for the tank to get filled up if both the inlet and the outlet pipes are left open.

8) In 1 minute, the cold water faucet fills up 1/11th of the tub and the hot water faucet fills up f8ills up 1/14th of the tub. Therefore, in 1 minute, both the  cold water faucet and hot water faucet willfill up 1/11 + 1/14 = 25/ 154 of the tub. Therefore, the two faucets, together, will fill up the tub in 154/25 = 6.16 minutes or in 6 minutes, 9.6 seconds.