During the first part of a trip, a canoeist travels 33 miles at a certain speed. The canoeist travels 2 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 4 hours. What was the speed on each part of the trip?

The speed on the first part of the trip was _____mph

Let the speed on the first part of the trip be x.

33/x+2/(x-5)=4
Solve for x and reject any solution less than x=5 mph.

To find the speed on each part of the trip, we can set up two equations using the given information.

Let's call the speed on the first part of the trip "x" mph.

The distance traveled on the first part of the trip is 33 miles, so we can set up the equation:
Distance = Speed x Time
33 = x(t1)
where t1 is the time taken on the first part of the trip.

The speed on the second part of the trip is 5 mph slower than the first part, so it is (x - 5) mph.

The distance traveled on the second part of the trip is 2 miles, so we can set up the equation:
Distance = Speed x Time
2 = (x - 5)(t2)
where t2 is the time taken on the second part of the trip.

The total time for the trip is given as 4 hours, so we can set up another equation:
t1 + t2 = 4

Now we have a system of two equations:
33 = x(t1)
2 = (x - 5)(t2)
t1 + t2 = 4

To solve this system of equations, we can use substitution or elimination method. Given that we have already solved for the speed on the first part, we can use substitution.

From the first equation, t1 = 33/x. Substitute this into the third equation:
33/x + t2 = 4

To solve for t2, multiply both sides by x:
33 + t2x = 4x

Now, let's isolate t2:
t2x - 4x = -33
x(t2 - 4) = -33
t2 - 4 = -33/x
t2 = -33/x + 4

Now we have an expression for t2. Let's substitute this into the second equation:
2 = (x - 5)(-33/x + 4)

Simplify this equation:
2 = (-33 + 4x - 165/x + 20)

Combine like terms:
2 = (4x - 165 - 165 + 20)/x
2 = (4x - 310)/x

Cross-multiply:
2x = 4x - 310

Subtract 2x from both sides:
310 = 2x

Divide both sides by 2:
x = 155

Therefore, the speed on the first part of the trip was 155 mph.