Justin's boat travels 175 km downstream in 5 hours and it travels 189 km upstream in 7 hours. Find the speed of the boat in still water and the speed of the stream's current.
since distance = speed * time, if the boat has speed b in still water, and the stream has speed s, we have
5(b+s) = 175
7(b-s) = 189
now solve as usual
idkk
To find the speed of the boat in still water (let's call it B) and the speed of the stream's current (let's call it C), we can use the formula:
Downstream speed = B + C
Upstream speed = B - C
Given the information in the problem, we can set up two equations:
175 km/5 hours = B + C (equation 1)
189 km/7 hours = B - C (equation 2)
Let's solve these equations simultaneously to find the values of B and C.
To start, let's simplify equation 1:
175 km/5 hours = B + C
35 km/h = B + C (equation 3)
Similarly, let's simplify equation 2:
189 km/7 hours = B - C
27 km/h = B - C (equation 4)
Now we have two linear equations:
B + C = 35 km/h (from equation 3)
B - C = 27 km/h (from equation 4)
We can solve these equations using the method of elimination.
By adding equations 3 and 4, we can eliminate the variable C:
(B + C) + (B - C) = 35 km/h + 27 km/h
2B = 62 km/h
Now, divide both sides of the equation by 2:
2B/2 = 62 km/h/2
B = 31 km/h
So, the speed of the boat in still water is 31 km/h.
Next, we can substitute this value back into either equation 3 or 4 to find the speed of the stream's current.
Let's use equation 3:
B + C = 35 km/h
31 km/h + C = 35 km/h
Now, subtract 31 km/h from both sides of the equation:
C = 35 km/h - 31 km/h
C = 4 km/h
Therefore, the speed of the stream's current is 4 km/h.
In conclusion, the speed of the boat in still water is 31 km/h and the speed of the stream's current is 4 km/h.