It takes 4.5 hours for a ship moving downriver to get from port A to port B. The return journey takes 6.3 hours. The river flows at 40 meters per minute. What is the distance between the two ports? (Give your answer in kilometers. 1 km = 1,000 meters)
The speed of the river is ... .. (40 m/min)*(60 min/h)*((1 km)/(1000 m)) = 2.4 km/h
speed = distance/time Let d represent the distance between the ports. Let s represent the speed of the ship. Downstream, we have .. s +2.4 = d/4.5 .. s = d/4.5 -2.4 Upstream, we have .. s -2.4 = d/6/3 .. s = d/6.3 +2.4
Now, we have the speed of the ship represented two ways. We assume the speed of the ship doesn't vary. so these are equal. .. (d/6.3) +2.4 = (d/4.5) -2.4 .. 4.8 = d(1/4.5 -1/6.3) = d(4/63) . . . . . rearrange and simplify .. 75.6 = d . . . . . . . . . . . . . . . . . . . . . . .multiply by 63/4
