Word Problem help?

Question

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

Answer 1

let x be the speed on the first part of the trip
on the second part of the trip, the speed is 4 km/hr slower.
So x - 4 is the speed on the second part of the trip

d = rt <==> t = d/r

the time it takes to cover 60km is 60/x
the time it takes to cover 24 km is 24/(x-4)

given the total time is 8hrs

60/x + 24/(x-4) = 8

now just solve and you'll get x = 12 km/hr

first part of the trip: 12 km/hr
second part of the trip: 8 km/hr

hope it helps
Rec

Answer 2

Let x= the speed for the first part of the trip.
The distance is 60 km.
Since D=RT, the time taken for this part of the trip
is T=D/R, or 60/x
For the second leg, R=x-4 and D =24
Therefore on this leg, T=24/(x-4)
The total time is 8 hr.
Therefore 60/x + 24/(x-4)=8
[60(x-4)+24(x)]=8(x-4)(x)
60x-240+24x=8x^2-32x
8x^2-32x-60x-24x+240=0
8x^2-116x+240=0
Dividing by 4, 2x^2-29x+60=0
(2x-5)(x-12)=0
For (2x-5)(x-12) to multiply out to 0,
Either (2x-5)=0, x=5/2
Or x-12=0, x=12

If x=5/2, that says he covered the first 60 km at 21/2
km per hour, THEN slowed down to 21/2-4 or -11/2
km per hour for the second leg of his trip. This makes no sense, so we discard this as an answer.
If x=12, then the second leg was covered at (12-4), or 8km/hr.

There is another way to justify discarding the 5/2
answer.
If the rate x was truly 5/2 km/hr for the first leg, then the time required to travel the first 60 km. is
T=D/R, =60/2.5, =24 hours. Since the entire trip took
only 8 hrs, 5/2 is not an acceptable answer to the
problem, It's a mathematical solution, but not a
practical one.

Answer 3

time x rate = 60
(8 - time) x (rate -4) = 24

5 hrs at 12 kph = 60
3 hrs at 8 kph = 24
8 total hours