Answer:
15 mph
Step-by-step explanation:
Given: Boat took 2 hours to reach Town A going upstream.
Speed of stream= 3 mph
Time taken to reach back home= 1 hours 20 minutes
Lets assume distance covered one side be "d" and speed of boat in still water be "s".
∴ Speed of boat in upstream= [tex](s-3) \ mph[/tex]
Speed of boat in downstream= [tex](s+3)\ mph[/tex]
Also converting into fraction of time taken to reach back home.
Remember; 1 hour= 60 minutes
∴ Time taken to reach back home= [tex]60+20= 80\ minutes[/tex]
Converting time given into fraction= [tex]\frac{80\ minutes}{60\ minutes} = \frac{4}{3} \ hours[/tex]
hence, Time taken to reach back home is [tex]\frac{4}{3} \ hours[/tex]
Now forming equation of boat travelling upstream and downstream, considering distance remain constant.
We know, [tex]Distance= speed \times time[/tex]
⇒ [tex](s-3)\times 2= (s+3)\times \frac{4}{3}[/tex]
Using distributive property of multiplication
⇒[tex]2s-6= \frac{4}{3}s +4[/tex]
subtracting both side by [tex]\frac{4}{3} s[/tex]
⇒[tex]2s-\frac{4}{3} s-6= 4[/tex]
Adding both side by 6
⇒ [tex]2s-\frac{4}{3} s= 10[/tex]
taking LCD as 3
⇒ [tex]\frac{2}{3} s= 10[/tex]
Multiplying both side by [tex]\frac{3}{2}[/tex]
⇒[tex]s= \frac{3}{2} \times 10[/tex]
∴s= 15 mph
Hence, 15 mph is the speed of the boat in still water.
