Answer:
Speed of boat in still water = 40 mph
Rate of current = 10 mph
Step-by-step explanation:
Let the speed of boat in still water be x & let the speed of the stream be y.
Total Distance = 150 miles
Time taken to travel during upstream = 5 hrs
Speed of the boat during upstream = [tex]\frac{150}{5} = 30\:mph[/tex]
Speed of boat during upstream can be represented as [tex]x - y = 30[/tex] because the boat is moving in the opposite direction of flow of stream.
Time taken to travel during downstream = 3 hrs
Speed of boat during downstream = [tex]\frac{150}{3} = 50\:mph[/tex]
Speed of boat during downstream can be represented as [tex]x+y=50[/tex] because the boat is moving in the same direction of flow of stream.
We got a pair of linear eqns. Let [tex]x-y=30[/tex] be eqn.1 and [tex]x+y=50[/tex] be eqn.2 . Using substitution method ,
From eqn.1 , [tex]x-y=30[/tex]
[tex]=> x = y + 30[/tex]
Putting 'x' in eqn.2 , [tex]x + y = 50[/tex]
[tex]=> y + 30 + y = 50[/tex]
[tex]=> y + y = 50-30[/tex]
[tex]=> 2y = 20[/tex]
[tex]=> y = \frac{20}{2} = 10\: mph[/tex]
Putting y in eqn.1 ,
[tex]x - 10 = 30[/tex]
[tex]=> x = 30 + 10 = 40 \:mph[/tex]
Hence , the speed of boat in still water is 40 mph and speed of stream is 10 mph
