A tour boat on a river traveled 40 miles downstream in 4 hours. The return trip against the current took 5 hours. What was the rate of the current?
A. 2.0 MPH
B. 1.5 MPH
C. 0.5 MPH
D. 1.0 MPH
I do not get this so it would be great for some help. Thank you!
let the speed of the boat in still waters be x mph
let the speed of the current be y mph
So going downstream or with the current the speed is x+y
going against the current the speed is x-y
so 40/(x+y) = 4
4x + 4y = 40
x + y = 10 , #1
and
40/(x-y) = 5
5x - 5y = 40
x-y = 8 , #2
add#1 and #2
2x = 13
x = 6.5
in #1
6.5 + y = 10
y = 3/5
Therefore ....
that last line should say y = 3.5
I still do not understand it that well... I get what you did then I get confused at y=3/5.
Oh ok, that made a lot of sense. Thank you so much. Once you cleared it up.
To find the rate of the current, we can set up a system of equations using the given information.
Let's represent the rate of the boat in still water as "b" and the rate of the current as "c". Since the boat is traveling downstream with the current, the effective speed will be the sum of the boat's speed and the current's speed. Similarly, when the boat is traveling upstream against the current, the effective speed will be the difference between the boat's speed and the current's speed.
For the downstream trip:
Distance = Rate × Time
40 miles = (b + c) × 4 hours
For the upstream trip:
Distance = Rate × Time
40 miles = (b - c) × 5 hours
Now we can solve this system of equations to find the values of b and c.
First, let's simplify the equations:
1. 40 = 4b + 4c
2. 40 = 5b - 5c
We can now solve for b or c by eliminating one variable.
Multiply equation 1 by 5 and equation 2 by 4 to make the coefficients of b equal:
1. 200 = 20b + 20c
2. 160 = 20b - 20c
Add the two equations together to eliminate b:
200 + 160 = 40b
360 = 40b
Divide both sides by 40:
9 = b
Now that we have the value of b, we can substitute it into either equation to find c. Let's use equation 1:
40 = (9 + c) × 4
40 = 36 + 4c
4c = 40 - 36
4c = 4
c = 1
So, the rate of the current is 1 mile per hour.
Therefore, the correct answer is B. 1.5 MPH.