Tiêu đề MSTE 3 Solutions.pdf ✅

▣ 8. A motorboat goes 5 km upstream in the same time it requires to go 7 km downstream. If the river flows at 2 kph, find the speed of the boat in still water. [SOLUTION] Let x be the speed of the boat. Upstream speed: x-2, Downstream speed: x+2 Time = Distance Speed t = 5 km x − 2 = 7 km x + 2 x = 12 kph ▣ 9. Two pipes are used to fill a water storage tank. The first pipe can fill the tank in 4 hours, and the two pipes together can fill the tank in 2 hours less than the second pipe alone. How long would it take for the second pipe to fill the tank? [SOLUTION] Let x be the time that the second pipe fills the tank. Its rate is 1/x. Rate × Time = Work Time = Work Rate t1 − t2 = 2 x − 1 1 4 + 1 x = 2 x = 4 hours “CLOCK PROBLEMS” VIDEO • It is between 3 and 4 o’clock, and in 20 minutes, the minute hand will be as much after the hour hand as it is now behind it. What is the time? [SOLUTION] In terms of minutes, the gap between the hour hand and the minute hand now is θ = (15 + x 12) − x = 15 − 11x 12 After 20 minutes, the gap becomes θ = (x + 20) − (15 + x + 20 12 ) = 11 12 (x + 20) − 15 Since the gap is the same in the two conditions,
15 − 11 x 12 = 11 12 ( x + 20 ) − 15 x = 6.3636 min The time is 3: 06 pm .