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?
Answers
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