solve problems using linear systems

Question

Tyler rows 10 km downstairs in 2h. On the return trip, it takes him 4 h to travel 8 km. Determine his average rowing speed and the speed of the current.

Answer 1

Distance=speed X time, so time=distance/speed. If Tyler's speed is s and the current is c, then the combined speed downstream (with the current) is s+c but upstream it's s-c. The times are 10/(s+c)=2 and 8/(s-c)=4. So 10=2s+2c and 8=4s-4c. These equations can be simplified: 5=s+c and 2=s-c. Add them together: 7=2s, so s=3.5 and therefore c=1.5, both speeds in km/hr.