During the first part of a trip a canoeist travels 49 miles at a certain speed. The canoeist travels 25 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip is 5hrs. What was the speed on each part of the trip?

speed on first part --- x mph

time for first part = 49/x hrs

speed of second part = x-5 mph , where x > 5
time for second part = 25/(x-5)

49/x + 25/(x-5) = 5
multiply by x(x-5)
49(x-5) + 25x = 5x(x-5)
49x - 245 + 25x = 5x^2 - 25x
5x^2 - 99x + 245 = 0
x = (99 ± √4901)/10
= 16.9 or 2.9 but x > 5

on the first trip he went at 16.9 mph and on the second part 11.9 mph

WoW! 16.9 mph in a canoe!!
I am a canoist, don't know anybody who can paddle that fast.

Thank you!

To solve this problem, we can use the concept of distance, speed, and time. We know that the total distance covered during the trip is the sum of the distances covered on each part of the trip.

Let's label the speed of the canoeist on the first part of the trip as 'x' mph. According to the problem, the canoeist traveled 49 miles at this speed. Therefore, the time taken for the first part of the trip is 49 miles divided by 'x' mph, which is 49/x hours.

The speed on the second part of the trip is given as 5 mph slower than the first part. So the speed on the second part is (x - 5) mph. The distance covered on the second part is 25 miles. Therefore, the time taken for the second part of the trip is 25 miles divided by (x - 5) mph, which is 25/(x - 5) hours.

The total time for the trip is given as 5 hours. This means that the time for the first part plus the time for the second part equals 5 hours:

49/x + 25/(x - 5) = 5

To solve this equation, we can cross-multiply and rearrange terms to get a quadratic equation:

49(x - 5) + 25x = 5x(x - 5)

Expanding and simplifying this equation gives:

49x - 245 + 25x = 5x^2 - 25x

Combining like terms:

74x - 245 = 5x^2 - 25x

Rearranging the terms and setting the equation equal to zero:

5x^2 - 99x + 245 = 0

To solve this quadratic equation, we can either factor it, complete the square, or use the quadratic formula. In this case, factoring is not straightforward, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In the equation we have, a = 5, b = -99, and c = 245. Plugging these values into the quadratic formula gives:

x = (-(-99) ± √((-99)^2 - 4*5*245)) / (2*5)

Simplifying:

x = (99 ± √(9801 - 4900)) / 10

x = (99 ± √4901) / 10

So the two possible values for 'x' are:

x = (99 + √4901) / 10

x ≈ 10.71 mph

or

x = (99 - √4901) / 10

x ≈ 4.29 mph

Therefore, there are two possible speeds for the two parts of the trip:

1) The speed on the first part of the trip is approximately 10.71 mph, and the speed on the second part is approximately 5.71 mph slower, which is approximately 5 mph.

2) The speed on the first part of the trip is approximately 4.29 mph, and the speed on the second part is approximately 4.29 mph slower, which is approximately 0 mph.

Note that the second possibility does not make sense since it means the canoeist is not moving on the second part of the trip. Therefore, the answer is that the speed on the first part of the trip is approximately 10.71 mph, and the speed on the second part is approximately 5 mph.