Answer:
1.1 hour or 1 hour and 6 minutes
Step-by-step explanation:
Time is given by the distance divided by the velocity. If the time it takes the tugboat to travel 20 km downstream in the same time it takes it to travel 10 km upstream, then:
[tex]t_1=t_2\\\frac{20}{v_b+v_c}=\frac{10}{v_b-v_c}\\v_c=5\ km/h\\20v_b-100=10v_b+50\\10v_b=150\\v_b=15\ km/h[/tex]
The velocity of the boat is 15 km/h. When traveling downstream, the current will favor the boat, therefore, the time required for it to travel 22 km downstream is:
[tex]t=\frac{22}{v_b+v_c} \\\t=\frac{22}{15+5}\\ t=1.1\ hour[/tex]
It will take the boat 1.1 hour or 1 hour and 6 minutes.
