Answer:
x = 3.5 hours
y = 1.5 hours
Explanation:
There are two unknowns, x and y, both in umits of hours. We need at least two equations before we start trying to solve this with substitution. Looking at the information, this should be possible.
First, we know that Speed x Time = Distance.
The distance covered by the cyclyst would be the sum of (12km/h)*x and (16km/h)*y, where x is the time, in hours, for the slower speed and y for the faster. Together, the student travels 66 km.
The total distance of 66 km would be comprised of the two distances 12x and 16y:
12x + 16y = 66 km
For the second equation, we know that the total time is 5 hours. That would be the sum of x and y:
x + y = 5 hours
We now have 2 equations, so we stand a good chance of finding the answer. Pick one of the equations and isolate one of the variables to one side. Let's choose x + y = 5 hours, since that is easy to rearrange:
x = 5-y
Now take the first equation and substitute the definition of x from above (5-y):
12x + 16y = 66
12(5-y) + 16y = 66
60-12y + 16y = 66
4y = 66-60
4y = 6
y = (6/4) or 1.5 h
The time spent at 16 km/h was 1.5 hours.
Use this value of y in either equation to find x. Let's use x+y=5, since that will be easier:
x+y = 5 for y = 1.5
x+1.5 = 5
x = 3.5h
The time spent at 12 km/h was 3.5 hours