the speed of a river current is 5 km/h..a boat travels 3 hours downstream and covers 5 km more than the distance covered in four hour upstream. find the boat speed in still water

Answer 1

Visualize this problem in your head: the river is flowing at 5 km/h while a boat is traveling both upstream and downstream, we can define the speed of the boat as "S" (km/h), and label the flow of the river as "F" = 5 (km/h). When the boat is traveling downstream, the flow of the river is working in the same direction with the boat to make it travel much faster than its typical speed, when the boat is traveling upstream, the flow of river is working in the opposite direction with the boat to make it travel much slower than its typical speed (this is similar to how if you walk WITH an escalator you will move faster than stairs, and if you walk AGAINST an escalator you will travel considerably slow).

We can define two sides of an equation as follows

Let H_D = 3 Hours (h)

Let H_u = 4 Hours (h)

Let S = Speed of Boat (km/h)

Let F = Flow of River (km/h)

Let D_D = Distance Traveled Downstream (km)

Let D_U = Distanced Traveled Upstream (km)

D_D = (H_D)*(F)+(H_D)*(S)

D_U = (H_U)*(F)-(H_U)*(S) Note: you subtract the speed when traveling upstream because it opposes the direction of flow

D_{D =} D_U + 5

Now all you need to do is plug in your values

(H_D)*(F)+(H_D)*(S) = (H_U)*(F)-(H_U)*(S) + 5

(3 hours) * (5 km/hour) + (3 hours) * S = (4 hours) * (5 km/hour) - (4 hours) * S + 5

15 + 3S = 20 - 4S + 5

Simplify this further

3S = 5 - 4S + 5

3S = 10 - 4S

7S = 10

Therefore, S = 10/7 = 1.42 (km/hour)

Remember to check your answer to ensure it is correct:

D_D = (H_D)*(F)+(H_D)*(S) = (3 hours) * (5 km/hour) + (3 hours) * (1.42 km/hour) = 19.28km

D_U = (H_U)*(F)-(H_U)*(S) = (4 hours) * (5 km/hour) - (4 hours) * (1.42 km/hour) = 14.28km

19.28 km is 5km more than 14.28km, therefore our value for speed is correct.