A boat travels upstream (against the current) between two points on a river $10$ mi apart in $2.5$ Hours. The return trip downstream takes only $45$ Minutes. What is the boat's speed, and how fast does the current in the river flow?
A)The speed of the boat is $4.5$ Mi/h and the speed of the current flow is about $8.4$Mi/h
B)The speed of the boat is $8.7$ Mi/h and the speed of the current flow is about $4.7$ Mi/h
C)The speed of the boat is $6.7$ Mi/h and the speed of the current flow is about $8.7$ Mi/h
D)The speed of the boat is $5$ Mi/h and the speed of the current flow is about $4$ Mi/h
E)The speed of the boat is $13.7$ Mi/h and the speed of the current flow is about $6.7$ Mi/h.

Question

Quizplus · Accepted Answer

Let's assume that the speed of the boat is $b$ and the speed of the current is $c$.

When the boat travels upstream, its effective speed is $(b-c)$ since it's going against the current. Therefore, we have the following equation: $$10 = 2.5(b-c)$$

When the boat travels downstream, its effective speed is $(b+c)$ since it's moving with the current. Therefore, we have the following equation: $$10 = \frac{3}{4}(b+c)$$

Now we have two equations with two unknowns. Solving for $b$ and $c$, we get:

$$b=8.7 	ext{ Mi/h} 	ext{ and } c=4.7 	ext{ Mi/h}$$

Therefore, the correct answer is (B).

A Boat Travels Upstream (Against the Current) Between Two Points 101010

A Boat Travels Upstream (Against the Current) Between Two Points $10$