Question

The motorboat covers a certain distance downstream in a river in 5 hours. It cover the same distance upstream in 5 hours and a half. Find the speed of boat in still water. The the speed of the stream is 1.5 km/hr.

Answer 1

let the speed of boat be X km/h
and the still water is 1.5 km/h
distance taken is y km/h


time travel to downstream be 5 hr/s
and the time taken by upstream be 5.5 hr/s

speed = distance / time

x+1.5= y/5
(x+ 1.5)5=y
5x +7.5=y.......(1)

CASE 2


x+1.5=y/5.5
(x+1.5)5.5=y
5.5x +6.25 =y .......(2)


from equation 1 and 2

5x + 7.5 =y

5.5x +6.25 =y


solve this equation and you will get your answer

Answer 2

Answer:

$\sf{31.5 km/hr}$

Step by step explanation:

Let the speed of the boat in still water be x.

Then,

Downstream                                             Upstream

Speed = (x + 1.5) km/hr                             Speed = (x - 1.5) km/hr

Time = 5 hrs                                              Time = 5.5 hrs.

Distance = S × T                                        Distance = S × T

               = (x + 1.5) × 5                                              = (x - 1.5) × 5.5

               = 5x + 7.5                                                   = 5.5x - 8.2

__________________________________________________________

Distance in Upstream = Distance in Downstream

⇒ 5.5x - 8.2 = 5x + 7.5  

⇒ 5.5x - 5x = 7.5 + 8.2

⇒ 0.5x = 15.7

⇒ x = 15.7/0.5

⇒ x = 31.5 km/hr

Hence, Speed of boat = 31.5 km/hr