A boat cruises 36 miles against a 3 mph current and 36 miles back in the direction of the same current. The round trip takes 5 hours. What is the speed of the boat in the still water?
use d=rt
Let V be the boat speed (with respect to water) and v=3 be the river speed.
36/(V+v) + 36(V-v)
=36/(V+3) + 36(V-3)
= 5 hours
Solve for V. You will get a quadratic equation. Take the positive root.
[36(V-3) + 36(V+3)]/(V^2-9) = 5
5V^2 -72V -45 = 0
(V-15)(5V +3) = 0
V = 15 mph
let speed of boat be x mph
time against current = 36/(x-3)
time with current = 36/(x+3)
solve
36/(x-3) + 36/(x+3) = 5
hint: multiply each term by (x+3)(x-3) to get a quadratic.
To find the speed of the boat in still water, we can solve this problem using the formula d = rt, where d is the distance, r is the rate or speed, and t is the time.
Let's break the problem into two parts:
1. The boat cruises 36 miles against a 3 mph current.
2. The boat cruises 36 miles in the direction of the same current.
Let's solve for each part separately:
1. Against the current (upstream):
Let's assume the speed of the boat in still water is represented by b mph. Since it's moving against a 3 mph current, the effective speed of the boat will be b - 3 mph. The distance is given as 36 miles.
Therefore, we can write:
36 = (b - 3) * t₁
where t₁ represents the time taken to go 36 miles against the current.
2. In the direction of the current (downstream):
The speed of the boat in the direction of the current will be b + 3 mph (since the boat and the current will add up). The distance is still 36 miles.
Therefore, we can write:
36 = (b + 3) * t₂
where t₂ represents the time taken to go 36 miles in the direction of the current.
Now, we know that the total time for the round trip is 5 hours. So, we can write:
t₁ + t₂ = 5
Now, we have a system of equations that we can solve to find the speed of the boat in still water (b).
Let's solve this system of equations using substitution or elimination method:
From the first equation:
t₁ = 36 / (b - 3)
Plug this into the second equation:
36 = (b + 3) * (36 / (b - 3))
Now, let's simplify this equation to solve for b.
Multiplying both sides by (b - 3):
36 * (b - 3) = (b + 3) * 36
36b - 108 = 36b + 108
36b - 36b = 108 + 108
0 = 216
We obtain a contradiction. The equation has no solutions, which means there is no value of b that satisfies the given conditions. It seems there might be an error or inconsistency in the question provided. Please double-check the question or provide any additional information if available.