Question

18. Susy is rowing a boat. She takes 6 hours to row 48 km upstream whereas she takes 3 hours to go the same distance downstream.

(i) 62 : 47

Based on the above situation, answer the following questions: (a) What is her speed of rowing in still water?

(i) 8 km/h (ii) 12 km/h

(b) What is the speed of the stream?

(1) 6 km/h (ii) 4 km/h

(iii) 10 km/h

(iii) 8 km/h

(iv) 16 km/h

(iv) 12 km/h

(c) If the speed of a boat in still water be 15 km/h and speed of the stream is 3 km/h u much time will a person take to travel 45 km downstream?

(ii) 3 h

(iii) 3.75 h

(iv) 4.5 h

(i) 2.5 h (d) A girl walks at the speed of 6 km/h in still air. If there is a strong breeze blowing at the

speed of 1.5 km/h. What would her speed be if she is walking against the breeze?

(1) 7.5 km/h (ii) 6.5 km/h

(iii) 4.5 km/h

(e) How much time will she take to walk 15 km if she is walking

(i) 2 h

(ii) 1.5 h

(iii) 1 h

(iv) 1.5 km/h

the wind?

(iv) 0.5​

Answer 1

Answer:

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

Let the speed of the stream be y km/hr

The speed of the boat downstream = (x+y) km/hr

The speed of the boat upstream = (x−y) km/hr

Time=

Speed

Distance

6 hours to travel 8 km upstream and 32 km downstream,

i. e 6=

x−y

8

+

x+y

32

(1)

7 hours to travel 20 km upstream and 16 km downstream.

i.e 7=

x−y

20

+

x+y

16

(2)

Let

x−y

1

=a and

x+y

1

=b

∴6=8a+32b ...(3)

7=20a+16b ...(4)

Answer 2

Answer:

Step-by-step explanation:

Given,

Susy takes  6 hours to row 48 km upstream

Susy takes 3 hours to row 48 km downstream.

Recall the formula

$speed = \frac{distance}{time}$

Solution:

Let speed of boat in still water = x km/hour

and speed of the stream = y km/hour

Speed downstream = (x+y) km/hour

Speed upstream = (x-y) km/hour

Since time taken to travel 48km upstream = 6hours, then speed upstream = $\frac{48}{6}$ = 8km/h

Time taken to travel 48km downstream = 3hours, then speed down stream = $\frac{48}{3}$ = 16km/hour.

Since speed upstream is (x-y), and speed downstream is (x+y) we have

x - y = 8 ----------------(1)

x + y = 16 ---------------(2)

(a) Adding equations(1) and (2) we get

2x = 24

x = 12

Speed in still water =x= 12km/h

(b) Substituting the value of x in (2) we get

12+y  = 16

y = 16 -12 = 4km/h

Speed of the boat = 4km/h

(c) Given,

Speed of boat in still water = x = 15km/h

Speed of stream = y = 3km/h

Speed downstream = x+y = 15 +3 = 18km/h

Time required to travel 45km downstream = $\frac{45}{18}$ = 2.5hours

(d)  Speed of  of girl in still air = 6 km/h

Speed of breeze = 1.5km/hour

Speed against the breeze = 6 - 1.5 = 4.5km/h

(e) Speed in the direction of wind = 6+1.5 = 7.5km/h

Time taken to travel 15km = $\frac{15}{7.5}$ = 2hours

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