SOLUTION: In a boat race, Jenny's team rowed their boat from point a to point b and back to point a. Points a and b are 30 miles apart. during the race there was a constant current flowing f
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Question 1107225: In a boat race, Jenny's team rowed their boat from point a to point b and back to point a. Points a and b are 30 miles apart. during the race there was a constant current flowing from a to b. she took 2 hours to travel from a to b and 2.5 hours to travel from b to a.
a)Calculate the speed of the boat from a to b and the speed from b to a.
b)find the speed of the boat from a to b if there was no current.
c) find the speed of the current. Answer by ikleyn(52858) (Show Source):
One way distance is 30 miles.
Downstream travel took 2 hours.
Upstream travel took 2.5 hours.
The effective speed downstream was = 15 miles per hour. (Speed = ).
The effective speed upstream was = 12 miles per hour. (Speed = ).
The effective speed downstream is u + v, where u is the speed of the boat in still water and v is the current speed.
The effective speed upstream is u - v.
Thus you have this system of two equations:
u + v = 15, (1)
u - v = 12. (2)
Add the equations (both sides). You will get
2u = 15 + 12 = 27 ====> u = = 13.5.
Thus we just found the speed of the boat in still water u = 13.5 mph.
Then from eq(1), v = 15 - 13.5 = 1.5 mph.
Answer. The effective speed of the boat downstream is 15 mph.
The effective speed of the boat upstream is 12 mph.
The speed of the boat in still water is 13.5 mph.
The speed of the current is 1.5 mph.
