Question

Sister Babys boat could attain a speed of 18 miles per hour on a lake. If the boat took the same time to go 132 miles down the river as it took to go 84 miles up the river, how fast was the current in the river

Answer 1

By setting up equations for the boat's speed going downstream and upstream, factoring in its speed in still water, and equating the times, we determined that the speed of the current in the river is 4 miles per hour.

Step-by-step explanation:

To find out how fast the current is in the river, we can set up equations based on the speed of the boat in still water and the effect of the current on the boat's speed when going downstream and upstream. Let's denote the speed of the current as c miles per hour.

When going downstream, the boat's speed relative to the shore is the sum of its speed in still water and the speed of the current (18 + c). When going upstream, the boat's speed relative to the shore is its speed in still water minus the speed of the current (18 - c).

Since the times for both trips are the same, we can express this relationship as:

Time downstream = 132 / (18 + c) = Time upstream = 84 / (18 - c)

Now we can set the two expressions equal to each other and solve for c:

132 / (18 + c) = 84 / (18 - c)

By cross-multiplication, we get:

132(18 - c) = 84(18 + c)

2376 - 132c = 1512 + 84c

216c = 864

c = 864 / 216

c = 4

The speed of the current in the river is 4 miles per hour.