During the first part of a trip, a canoeist travels 57 miles at a certain speed. The canoeist travels 13 miles on the second trip at a speed 5 mph slower. The total time for the trip is 5 hrs. what was the speed on each part of the trip?

The speed on the first part is?

The speed on the second part is? Someone was kind enough to help, but it did not work into the equation. Help? Please..

V1 = X mi/h on 1st part of trip.

t1 = d1/V1 = 57 / X hrs.

t2 = d2/V2 = 13 / (x-5) hrs.

t1 + t2 = 5 hrs.
57/x + 13/(x-5) = 5.
Multiply both sides by x(x-5).
57(x-5) + 13x = 5x(x-5).
57x - 285 + 13x = 5x^2 - 25x.
-5x^2 + 57x +13x +25x = 285.
-5x^2 + 95x = 285.
-5x^2 + 95x - 285 = 0.
Divide both sides by -5:
x^2 - 19x + 57 = 0.
Use Quadratic Formula.
X = 15.3 mi/h = Speed on 1st part of trip.
x-5 = 15,3-5 = 10.3 mi/h = Speed on 2nd
part of trip.

To solve this problem, let's start by assigning variables to the unknowns in the question.

Let's call the speed on the first part of the trip "s" (in mph).
Since the speed on the second part of the trip is 5 mph slower, we can represent it as "s - 5" mph.

Now, let's use the formula distance = speed * time to form two equations based on the given information:

1) For the first part of the trip:
distance = speed * time
57 = s * t1

2) For the second part of the trip:
distance = speed * time
13 = (s - 5) * t2

Since we want to find the speeds, the equations should be in terms of speed.

Now, let's express the time in terms of the speeds using the formula time = distance / speed:

1) For the first part of the trip:
t1 = 57 / s

2) For the second part of the trip:
t2 = 13 / (s - 5)

We also know that the total time for the trip is 5 hours:
t1 + t2 = 5

Now we can substitute the expressions for t1 and t2 into the equation for the total time:

57 / s + 13 / (s - 5) = 5

To solve this equation, we can multiply through by s(s - 5) to eliminate the denominators:

57(s - 5) + 13s = 5s(s - 5)

Now, simplify and solve for s:

57s - 285 + 13s = 5s^2 - 25s
70s - 285 = 5s^2 - 25s
0 = 5s^2 - 95s + 285

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula.

Once we solve the quadratic equation, we will get the values of s, which represent the speeds on each part of the trip.