Question

a steamer going downstream in a river covers the distance between two towns in 15 hours coming back upstream it cover this distance in 20 hours the speed of the water is 3 kilometre per hour find the distance between two towns​

Answer 1

Answer:

Distance between the two towns = 360 km.

Step-by-step explanation:

Given:

• Steamer going downstream covers the distance in 15 hours
• Steamer going upstream covers the distance in 20 hours
• Speed of the water = 3 km/hr

To Find:

• Distance between the two ports

Concept:

Form linear equations using the given datas. Solving it we get the value of distance.

Solution:

Let the speed of the steam be x km/hr

Hence,

Speed while going upstream = (x - 3) km/hr

Speed while going downstream = (x + 3) km/hr

Now we know that,

Distance = Speed × Time

Hence

While going upstream,

Distance = (x - 3) × 20

Distance = 20x - 60-------(1)

While going downstream,

Distance = Speed × Time

Distance = (x + 3) × 15

Distance = 15x + 45-----(2)

By given,

The distance between the two ports while going upstream and downstream are equal.

Hence LHS of equation 1 and 2 are equal, therefore RHS must also be equal.

20x - 60 = 15x + 45

20x - 15x = 45 + 60

5x = 105

x = 105/5

x = 21

Hence the speed of the steamer is 21 km/hr

Now substitute the value of x in equation 1,

Distance = 20x - 60

Distance = 20 × 21 - 60

Distance = 420 - 60

Distance = 360 km

Hence the distance between the towns is 360 km.

Answer 2

Given :

⠀⠀⠀⠀⠀⠀• Steamer going downstream covers the distance in 15 hrs

⠀⠀⠀⠀⠀⠀• Steamer going upstream covers th distance in 20 hrs

⠀⠀⠀⠀⠀⠀• The speed of the water is 3 km/hr

To find :

• Distance between two towns

Solution :

• By given the speed of the steamer is 3km/hr

Hence,

•Let assume the speed of the steamer as x km/hr

• Speed while traveling upstream = (x-3) km/hr

• Speed while traveling downstream = (x+3)km/hr

we know that

Distance = Speed × Time

Hence by the first case given

Distance = (x-3) × 20

Distance = 20x - 60 ____(¡)

By the second case given

Distance = (x+3) × 15

Distance = 15x + 45____(¡¡)

In equations i and ii , the distance travelled is same Therefore

=> 20x - 60 = 15x + 45

=> 20x - 15x = 45 + 60

=> 5x = 105

=> x = 21

Hence the speed of steamer is 21 km/hr

Now substitute the value of x in equation 1

Distance = 15x + 45

⠀⠀⠀⠀⠀⠀=15 × 21 + 45

⠀⠀⠀⠀⠀⠀=315 + 45

⠀⠀⠀⠀⠀⠀=360 km

Hence the distance between the two towns is 360 km.