Question: An excursion boat takes 1.5 times as long to go 360 miles up a river than to return. If the boat cruises at 15
miles per hour in still water, what is the rate of the current?

This question was asked before. Below is the best answer, but it doesn’t check out. By his math, the boat takes 4.8 hrs upstream and 1.6 downstream. That is not 1.5 as the question dictates. I can set the problem up, but have long forgotten the algebra to actually solve it. The problem is making me nuts. I want the answer and supporting equations please.

ORIGINAL WRONG ANSWER

I cannot believe the previous answers!
The length of the river is irrelevant. It’s all down to the speed of the river.
If the boat is traveling at 15mph from A to B for 1.5 hours it will travel 22.5miles in still water. If it travels 15mph from B to A for 1hour it will travel 15 miles. Therefore the speed of the river is 7.5 mph (the difference between 22.5 and 15).
Also doesn’t matter if it’s fresh water, sea water, mercury, a river of liquid nitrogen.

Hope this helps Bigpathome.
(river boat cruises)

Best answer:

Answer by Rec
distance = speed * time

let r be the rate of the current.

when the boat travels downstream, its resultant speed is 15+r. We don’t know the time it takes the boat to travel 360 miles, so we’re gonna t represent the time it takes the boat to travel 360mile.

so the speed is 15 + r
the time is t

use the formula above and you’ll get:
360 = (15 – r) 1.5t

Now that the boat travels upstream, its speed is 15 – r. It takes 1.5 times as long to travel upstream than downstream. We know the time it takes the boat t hours to travel downstream is t, then 1.5t is the time it takes the boat to travel upstream.

so the speed is 15 – r
time is 1.5t

360 = (15 + r)t

so you have two equations:
360 = (15 + r)*t
360 = (15 – r) * 1.5t

now just solve. Multiply
360 = 22.5t – 1.5rt
360 = 15t + rt

multiply the second equation by 1.5
360 = 22.5 – 1.5rt
1.5(360 = 15t + rt)

add the two equations
360 = 22.5t – 1.5rt
540 = 22.5t + 1.5rt
—————————-
900 = 45t
t = 20 hrs

plug the time back in to find the rate of the current
360 = (15 + r) 20
18 = 15 + r
r = 3

the rate of the current is 3 mi/hr.