Question

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of tug he river and the rate of the boat in still water respectively are?

Answer 1

Answer: rate of tug of the river = 7 miles per hour

rate of the boat = 17 miles per hour

Step-by-step explanation:

Let the speed of the boat be x miles per hour

Let the speed of the tug of the river be y miles per hour

Speed = distance / time

If a boat goes downstream 72 miles in 3 hours, the the speed is

72/ 3 = 24 miles per hour

Since the speed is higher than when it went upstream, it means that it moved in the same direction with the wind hence, it moved in still water.

The total speed would be x -y. Therefore

x + y = 24 - - - - - - -1

If a boat goes downstream 60 miles in 6 hours, the the speed is

60/ 6 = 10 miles per hour

Since the speed is lower than when it went downstream, it means that it moved in the opposite direction of the tug of the river.

The total speed would be x -y. Therefore

x - y = 10 - - - - - -2

Adding equation 1 and equation 2

2x = 34

x = 34/2 =17

y = 24 - x = 24 - 17

y = 7