Answer
Rate of canoe in calm water is 7 mph
Step-by-step explanation:
Let y be the rate of the canoe in calm water
Let z represent the rate of current
Traveling with the current, the canoe went 30miles in 3 hours
The total speed of the current and canoe will be (y + z) mph
Recall that,
speed = distance / time
Distance = speed x time
Distance = 30 miles
time = 3 hours
30 = 3( y + z)
divide through by 3
30/3 = 3/3 (y + z)
10 = y + z -------------------- equation 1
Against the current, the canoe went 12 miles in 3 hours
Let the speed = (y - z) mph
Distance = speed x time
12 = 3(y - z)
Divide through by = 3
4 = y - z ------------- equation 2
The two-equation can be solved simultaneously
y + z = 10 --------------- equation 1
y - z = 4 -------------- equation 2
Eliminate z by adding the two equations equation together
(y + y) + (z - z) = 10 + 4
2y + 0 = 14
2y = 14
y = 14/2
y = 7 mph
To find z, put y in equation 1
y + z = 10
z = 10 - y
z = 10 - 7
z = 3 mph
Hence, the rate of canoe in calm water is 7mph
