A boat travels upstream and after one hour has gone 10 km.The boat next travels downstream and after one hour has gone 18 km.If the boat's speed relative to the water is constant,what is the speed of the current in the river?
A)3 km/h
B)4 km/h
C)5 km/h
D)6 km/h
E)7 km/h

Question

Quizplus · Accepted Answer

Let's call the speed of the boat relative to the water "b" and the speed of the current "c".

When the boat is traveling upstream, it is going against the current, so its effective speed is b - c. We know that in one hour, the boat traveled 10 km, so:

b - c = 10

When the boat is traveling downstream, it is going with the current, so its effective speed is b + c. We know that in one hour, the boat traveled 18 km, so:

b + c = 18

Now we have two equations with two variables. We can solve for one of the variables by adding the two equations together:

(b - c) + (b + c) = 10 + 18
2b = 28
b = 14

Now we can plug in the value of b into one of the original equations to find c:

14 - c = 10
c = 4

Therefore, the speed of the current is 4 km/h, so the answer is B.

A Boat Travels Upstream and After One Hour Has Gone