A boat travels upstream and after one hour has gone 8 km.The boat next travels downstream and after one hour has gone 14 km.If the boat's speed relative to the water is constant,what is the speed of the current in the river?

A) 2 km/h
B) 3 km/h
C) 4 km/h
D) 5 km/h
E) 6 km/h

Question

A boat travels upstream and after one hour has gone 8 km.The boat next travels downstream and after one hour has gone 14 km.If the boat's speed relative to the water is constant,what is the speed of the current in the river?
​
A) 2 km/h
B) 3 km/h
C) 4 km/h
D) 5 km/h
E) ​6 km/h

Quizplus · Accepted Answer

The boat's speed relative to the water is constant. Let the speed of the boat be 'b' km/h and the speed of the current be 'c' km/h. Upstream, the effective speed is (b - c) km/h, and downstream, it is (b + c) km/h. Given that upstream the boat travels 8 km in 1 hour, we have b - c = 8. Downstream, the boat travels 14 km in 1 hour, so b + c = 14. Solving these two equations simultaneously:  b - c = 8  b + c = 14  Adding the equations: 2b = 22, so b = 11.  Substituting b = 11 into b - c = 8 gives 11 - c = 8, so c = 3 km/h.

A Boat Travels Upstream and After One Hour Has Gone