Question

Canoeing. during the first part of a canoe trip Ken covered 60km at a certain speed.He then traveled 24 km at a speed that was 4km/h slower.If the total time for the trip was 8 hrs.,what was the speed on each part of the trip?

Answer 1

Set up your equations. Let v be the speed of the first trip, t_1 the time taken in the first trip and t_2 the second time. Using the definition,\[speed=\frac{distance}{time}\]then\[distance=(speed)(time)\]For the first leg\[60=vt_1\]and the second\[24=(v-4)t_2\]We know also that \[t_1+t_2=8\]You have three equations in three unknowns which you can now solve.

Answer 2

\[t_2=8-t_1\]which you sub. into the equation 24=(v-4)... to get\[24=(v-4)(8-t)\]where I've dropped the subscript on t_1. So\[t=\frac{56-8v}{4-v}\]

Answer 3

Substitute this into the first equation,\[60=v(\frac{56-8v}{4-v}) \rightarrow 240-60v=56v-8v^2\]

Answer 4

This is quadratic in v\[8v^2-116v+240=0\]

Answer 5

which can be factored as\[4(v-12)(2v-5)=0\rightarrow v=12,\frac{5}{2}\]

Answer 6

If v=5/2, t=24 hours, which is outside your 8 hour limit. The other solution, v=12km/h yields t=5 hrs. So the first part of the trip took 5 hours, the second part therefore took the remaining 3 hrs.

Answer 7

Damn, I answered the wrong question.

Answer 8

Hey it looks good to me, I liked the step by step explanation. I am sure Anointed will appreciate it.

Answer 9

I like too

Answer 10

Agree, I learned something.

Answer 11

Cheers

Answer 12

Looks good to me.These kind of equations are a little complicated but you made it look so easy! Thanks!

Answer 13

You're welcome :)