Question

During the first part of a trip, a canoeist travels 57 miles at a certain speed. The canoeist travels 5 miles on the second part of the trip at a speed 5 mph slower. The total time of the trip is 3 hours. what was the speed on each part of the trip

Answer 1

i think you should try it first

Answer 2

first journey speed is 57/x
second journey speed (5/x)-5
equate time to get answer

Answer 3

distance = rate*time
Let x be original speed, t be time for 1st part of trip

57 = xt
5 = (x-5)(3-t)

solve system of 2 equations

Answer 4

use substitution:
t = 57/x

5 = (x-5)(3-57/x)
Now multiply both sides by x to get it out of denominator
5x = (x-5)(3x -57)
Distribute
5x = 3x^2-72x +285
set equal to 0
3x^2 -77x +285 = 0
use quadratic formula

x = 77 +-sqrt(77^2 - 4(3)(285)) / 6
x = 77 +- sqrt(2509)/6
x = 4.485 or 21.18

x must be greater than 5, since x-5 is speed on 2nd part of trip

x= 21.18
x-5 = 16.18