Answer: The speed of the boat in still water is 12.5 mph and the speed of the current is 2.5 mph
Step-by-step explanation:
Let x represent the speed of the motorboat in still water.
Let y represent the speed of the current.
The motorboat travels 60 km in 4 hours with the current. This means that the total speed of the motor boat would be (x + y) km/h.
Distance = speed × time
Distance travelled by the motorboat with the current is
60 = 4(x + y)
Dividing through by 4, it becomes
15 = x + y-- - - - - - - - - - -1
The motorboat travels 35 km in 3.5 hours against the current. This means that the total speed of the motorboat would be (x - y) km/h.
Distance travelled by the motorboat with the current is
35 = 3.5(x - y)
Dividing through by 4, it becomes
10 = x - y-- - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
25 = 2x
x = 25/2 = 12.5 mph
Substituting x = 12.5 mph into equation 1, it becomes
15 = 12.5 + y
y = 15 - 12.5
y = 2.5 mph
