Question

A motorboat travels 60 km in 4 hours with the current and 35 km in 3.5 hours against the current. Find the speed of the boat in still water and the speed of the current.
Please help...

Answer 1

Step-by-step explanation:

Distance = rate × time

If b is the speed of the boat in still water, and c is the speed of the current, then:

60 = (b + c) × 4

35 = (b − c) × 3.5

Simplifying:

15 = b + c

10 = b − c

Add the equations together:

25 = 2b

b = 12.5

Plug into either equation to find c:

c = 2.5

The speed of the boat is 12.5 km/h, and the speed of the current is 2.5 km/h.

Answer 2

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