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

Question

anonymous · Answer

Since you have two unknowns, you need two equations to solve this problem.

The first equation is fairly simple. It's just: x+y=8 Where x= the time for the first part of the trip and y= time for the second part of the trip,

The second equation is a little bit tricky. So let 60/x = speed of the first part. Let 24/y = the speed of the second part of the trip. Since the speed of the first part of the trip is equal to the speed of the second part of trip + 4 Km/hr, we can write the second equation is follows:

60/x = 24/y + 4

Now we have two equations; so we can now solve.

Rewrite the first equation to look like this: x=8-y 

Now substitute into the other equation.

60/(8-y) = 24/y +4

Multiply both sides by (8-y)

60 = (24/y +4) (8-y)

60 = (192-24y)/y +32 -4y

28 = (192 -24y)/y -4y

Multiply both sides by y

28y = 192 -24y -4y^2

4y^2 +52y -192

Solve for y using quadratic equation$$(-52\pm \sqrt{52^{2}-(4*4*-192)})/(2*4)$$

So y = 3 hours

So x = 8-3 or 5 hours

So the speed for the first part of the trip is 60km/5hr or 12km/hr 

The speed for the second part of the trip is 24km/3hr or 8 km/hr