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?

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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?

Mathematics
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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.
\[t_2=8-t_1\]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\[t=\frac{56-8v}{4-v}\]
Substitute this into the first equation,\[60=v(\frac{56-8v}{4-v}) \rightarrow 240-60v=56v-8v^2\]

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Other answers:

This is quadratic in v\[8v^2-116v+240=0\]
which can be factored as\[4(v-12)(2v-5)=0\rightarrow v=12,\frac{5}{2}\]
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.
Damn, I answered the wrong question.
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Agree, I learned something.
Cheers
Looks good to me.These kind of equations are a little complicated but you made it look so easy! Thanks!
You're welcome :)

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