Question

Speed of boat in still water is six times of speed
of stream. If boat covers 210 km in upstream in 7
hours, then find the downstream speed of boat?
(a) 42 km/hr. (b) 36 km/hr. C) 30 km/hr.
(d) 32 km/hr. (e) 24 km/hr.

Can somebody please tell me how it solved??

-thanku

Answer 1

Answer:

Step-by-step explanation:

★Speed of stream 2 km/hr

★Speed of boat

=

10 km/hr

Step-by-step explanation:

Given :

• Boat travels 32 km upstream and 36 km downstream in 7 hours • Boat travels 40 km upstream and 48 km downstream in 9 hours

To Find :

Speed of boat in still water

Speed of the stream

Solution :

Let the speed of boat in still water be x km/hr

Let speed of stream be y km/hr

Hence,

Speed of boat while travelling upstream = ( x - y) km/hr

Time taken is given by the equation,

Time = Distance/Speed

By first case given,

36 + x - y x + y

32

-> By second case given,

40 48 + Y x + y 9 -(2)

- Let us take 1/x-y as p and 1/x+y as q

- Hence equation 1 and

32p+36q = 7 -----(3)

40p + 48q = 9 ----(4)

Multiply equation 3 by 4 and equation 4 by 3

Hence we get,

128p + 144q = 28---(5)

120p + 114q = 27----(6)

Solving equation 5 and 6 by elimination method,

8p= = 1

p = 1/8

» Substitute the value of p in equation 4

40 x 1/8 + 48q = 9

5 + 489 = 9

48q = 4

q=1/12

- Now we know that p = 1/x-y and q =

1/x+y

Hence x-y = 1/p and x+y = 1/q

x - y = 8

x = 8 + y ----(7)

→ x+y=12

Substitute value of x from equation 7

8 + y + y = 12

2y = 4

Hence speed of stream is 2 km/hr

Speed of stream 2 km/hr

-

Substitute value of y in equation 7

X = 8+2

X = 10

- Hence the speed of boat in still water is 10 km/hr

Speed of boat 10 km/hr

Notes

A linear equation in two variables can be solved by

• Substitution method

• Elimination method

Cross multiplication method