Question

A boat goes 360 km upstream and returns
the same point in 35 hours. If the speed
of the current is 3 km/h, how much distance
boat will cover in still water in 6 hours?​

Answer 1

Answer:

A boat goes 35 km upstream and return the same point in 38 hours .If the current speed =3km/h

Step-by-step explanation:

boat distance will cover in still water in 6 hours =6 multiply 3 =18km

Answer 2

Answer:

Distance will cover by the boat in still water in 6 hours  = 21×6 = 126km

Step-by-step explanation:

Given,

The time taken by the boat to travel 360km upstream and returns to the same point = 35hours

Speed of the current =  3 km/h

To find,

Distance cover the boat in still water in 6hours

Recall the formula

Time = $\frac{distance }{speed}$

Solution

Let the speed of the boat in still water = x km/h

Since the speed of the current  is 3 km/h

Speed downstream = (x+3)km/h

Speed upstream = (x-3)km/h

Distance traveled by boat upstream = 360km

Distance traveled by boat downstream = 360km

Time taken to to travel 360km upstream = $\frac{360}{x-3}$

Time taken to travel 360km downstream = $\frac{360}{x+3}$

Since the total time taken to travel upstream and downstream is 35hours

$\frac{360}{x-3}$ +  $\frac{360}{x+3}$ = 35

$\frac{1}{x-3}$ + $\frac{1}{x+3}$ = $\frac{35}{360}$

$\frac{2x}{(x-3)(x+3)}$  = $\frac{35}{360}$

2x(360) = 35(x² -9)

35x² - 720x- 315 = 0

7x² - 144x- 63 = 0

7x² - 147x +3x -63 = 0

7x(x-21)+3(x-21) = 0

(7x+3)(x-21) = 0

x =$\frac{-3}{7}$ or x = 21

∴ Since speed is not negative, speed of the boat in still water  = 21km/h

That is,

distance will cover by the boat in still water in 1 hour = 21km

∴Distance will cover by the boat in still water in 6 hours  = 21×6 = 126km

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