Question

1. A motor boat can travel 45 km downstream in 2 h and 30 min; and 39 km
upstream in 3 h and 15 min. What is the speed of the boat in still water?
What is the speed of the current?​

Answer 1

Answer:

speed of boat in still water = 15 km/hr

speed of the current = 3 km/hr

Step-by-step explanation:

let the speed of boat in still water = x km/hr

speed of the current = y km/hr

A.T.Q

time = distance/speed

motor boat travel in downstream

then speed = x + y

2 + 30/60 = 45/(x+y)

2 + 1/2 = 45/(x+y)

(4+1)/2 = 45/(x+y)

5/2 = 45/(x+y)

5(x+y) = 45 × 2

5x + 5y = 90

divide by 5

x + y = 18 -----------(1)

motor boat travel in upstream

then speed = x - y

3 + 15/60 = 39/(x - y)

3 + 1/4 = 39/(x - y)

(12 + 1)/4 = 39/(x - y)

13/4 = 39/(x - y)

13(x - y) = 39 × 4

13x - 13y = 156

divide by 13

x - y = 12 ------------(2)

on adding eq. 1 and 2

x + y = 18

x - y = 12

2x = 30

x = 15

put x in eq.1

x + y = 18

15 + y = 18

y = 18 - 15

y = 3

speed of the boat in still water = 15 km/hr

speed of the current = 3 km/hr