during the first part of a trip a canoeist travels 56 miles at a certain speed. the canoeist travels 22 miles on the second trip at a speed 5 mph slower. the total time for the trip is 3 hrs. what was the speed on each part of the trip?

Question

radar · Answer

d=st where distance equal speed times time.
The time for the complete trip is 3 hrs.
Trip was in two parts where the time for each part would be:

56/speed for first leg
22/speed for  second leg
Let s = first leg speed
s-5 would be speed of second leg (given) then we have this equation
56/s + 22/(s-5) = 3 hrs.  The rest is algebra

radar · Answer

First using the LCD of s(s-5) add the left hand terms
(78s-280)/(s^2-5s)=3     Now cross multiply getting:
$$3s ^{2}-15s=78s-280$$Consolidate and put in standard form:$$3s ^{2}-93s+280=0$$

radar · Answer

Solve using the quadratic formula for speed.

radar · Answer

Using calculator I get speed of 27.62 for first leg and 22.62 for second leg.  Warning, something doesn't seem right, that is awful fast for paddling a canoe lol.  Check everything.

radar · Answer

@dumbcow, did I make an error?

radar · Answer

Sometimes the data furnished is not logical for the problem, this may be the case, plus they must of paddled fast!

radar · Answer

@Mertsj could you, at your leisure (of course) verify this solution?