Question

A boat goes 20 km upstream and 28 km downstream in 7 hours. In 8½ hours, it can go 28 km upstream and 21 km downstream.
A boat goes 20 km upstream and 28 km downstream in 7 hours. In 8½ hours, it can go 28 km upstream and 21 km downstream.

Let the speed of the boat in still water be x km/h and speed of the stream be y km/h. Then, the pair of equations will be
1 point
20/(x+y) + 28/(x-y) = 7; 28/(x+y) + 21/(x-y) = 8½
20/(x-y) + 28/(x+y) = 7; 28/(x-y) + 21/(x+y) = 8½
20/(y+x) + 28/(y-x) = 7; 28/(y+x) + 21/(y-x) = 8½
20/(y-x) + 28/(y+x) = 7; 28/(y-x) + 21/(y+x) = 8½

Answer 1

Answer:

Let speed of boat in still water be a km/hr.

Let rate of the current be b km/hr.

∴ Speed of the boat upstream =(a−b) km/hr.

∴

a−b

24

+

a+b

28

=6 ...(i)

and

a−b

30

+

a+b

21

=

2

13

..(ii)

From (i) and (ii), we have

a−b

1

=

6

1

and

a+b

1

=

14

1

⇒a−b=6 and a+b=14

⇒a=10 km/hr.