Question

Question 25 A motorboat travels 188 km in 4 hours going upstream. It travels 276 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current

Answer 1

The rate of the boat in still water is 58 km/h.

The rate of the current in still boat is 11 km/h.

Step-by-step explanation:

Given that,

Distance in upstream = 188 km

Distance in downstream = 276 km

Time = 4 hrs

We need to calculate the speed

Let x be the speed of boat in still water and y be the speed of current.

Speed of boat upstream= x-y

For upstream,

`x-y=(188)/(4)`

`x-y=47`

Speed of boat downstream= x+y

For downstream,

`x+y=(276)/(4)`

`x+y=69`

solve system of equation of x and y and we get

x=58 km/h and y=11 km/h

Hence, The rate of the boat in still water is 58 km/h.

The rate of the current in still boat is 11 km/h.

Answer 2

The rate of boat in still water is 58 km/h

and, the rate of water is 11 km/h

Step-by-step explanation:

Given:

While going upstream

distance = 188 km

Time = 4 hours

net speed of the motorboat = distance / time

thus,

the net upstream speed of the motorboat = ( 188 / 4) = 47 km/hr

now,

while moving in the downstream

distance = 276 km

Time = 4 hours

thus,

the net upstream speed of the motorboat = ( 276 / 4) = 69 km/hr

Let the rate of the water current be 'x' and the rate of motor boat in still water be 'y'

now, while moving upstream the rate of water will try to reduce the speed and while moving downstream the water current will add to the rate of the boat

thus,

for upstream the net rate = y - x = 47 km/h

and, for the downstream the net rate = y + x = 69 km/h

therefore on solving the above equations, we get

y - x = 47

- (y + x = 69 )

----------------------

0 - 2x = - 22

or

x = 11 km/h

substituting the value of x to find the y

we have

y - x = 47

or

y - 11 = 47

or

y = 58 km/h

hence,

the rate of boat in still water is 58 km/h and the rate of water is 11 km/h