A straight canal has motorboats departing from two terminals at opposite ends. The motorboats depart at regular intervals of T minutes in both directions and travel at a constant speed v . A tourist is riding a bicycle on a path parallel to the canal at a constant speed of 20 km/h . The tourist observes that a motorboat overtakes him every 18 minutes , and he crosses a motorboat moving in the opposite direction every

Step-by-step solution

Let the speed of the motorboats be v and the departure interval be T . The distance between two consecutive motorboats moving in the same direction is vT . The speed of the tourist is u = 20 km/h . When the motorboats overtake the tourist, they are moving in the same direction. The relative speed is v - u . The time interval between consecutive overtakes is 18 minutes . (v - 20) 18 60 = v T 60 vT = 18(v - 20) When the motorboats cross the tourist in the opposite direction, the relative speed is v + u . The time int