Question 169481
During the first part of a trip, a canoeist travels 37 miles at a certain speed.
 The canoeist travels 7 miles on the second part or the trip at a speed 5 mph
 slower. The total time for the trip is 4 hours. What is the speed on each part
 of the trip?
:
Let s = speed on the 1st part of the trip
then
(s-5) = speed on the 2nd part
:
Write a time equation: Time = {{{dist/speed}}}
:
1st part time + 2nd part time = 4 hrs
{{{37/s}}} + {{{7/((s-5))}}} = 4
:
Multiply equation by s(s-5) to get rid of the denominators, results:
37(s-5) = 7s = 4s(s-5)
:
37s - 185 + 7s = 4s^2 - 20s
:
44s - 185 = 4s^2 - 20s
:
Arrange as a quadratic equation
4s^2 - 20s - 44s + 185 = 0
:
4s^2 - 64s + 185 = 0
:
Use the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this problem x=s; a=4; b=-64; c=185
{{{s = (-(-64) +- sqrt(-64^2 - 4*4*185 ))/(2*4) }}}
:
{{{s = (64 +- sqrt(4096 - 2960))/(8) }}}
:
I'll let you do the math. You will get two positive solutions, but only one will make sense.

Check your solution by substituting for s in the original equation.