1.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
This is also another question I did not understand. Thank you.
(p + r)(4) = 40
(p -r) (5) = 40
p + r = 10
p -r = 8
2p = 18
p = 9
9 + r = 10
r = 1
= 1 MPH
To solve this problem, we can use the concept of relative motion. Let's assume the speed of the tour boat in still water is 'x' miles per hour (MPH), and the speed of the current is 'c' MPH.
When the boat is moving downstream (with the current), the effective speed of the boat will be the sum of its speed in still water and the speed of the current. Therefore, the effective speed downstream is 'x + c' MPH.
According to the information given, the boat travels 40 miles downstream in 4 hours. So, we can write the equation:
speed (downstream) = distance/time
(x + c) = 40/4
Simplifying this equation gives us:
x + c = 10
Similarly, when the boat is moving upstream (against the current), the effective speed of the boat will be the difference between its speed in still water and the speed of the current. Therefore, the effective speed upstream is 'x - c' MPH.
Again, according to the information given, the boat travels the same distance of 40 miles upstream in 5 hours. So, we can write the equation:
speed (upstream) = distance/time
(x - c) = 40/5
Simplifying this equation gives us:
x - c = 8
We now have a system of equations:
x + c = 10
x - c = 8
To solve this system, we can add these two equations:
(x + c) + (x - c) = 10 + 8
This simplifies to:
2x = 18
Dividing both sides by 2, we find:
x = 9
Now that we know the speed of the boat in still water, we can substitute this value back into one of the original equations to solve for the current speed:
x + c = 10
9 + c = 10
Simplifying this equation gives us:
c = 1
So, the rate of the current is 1.0 MPH, which corresponds to option D in the given choices.