Question

41.
A steamer, going downstream in a river, covers the distance between two towns
15 hours. Coming back upstream, it covers this distance in 20 hours. The speed
the water is 3 km/hr. Find the distance between two towns.
​

Answer 1

Answer:

Distance between the 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
• The speed of the water is 3 km/hr

To Find:

• Distance between the two towns

Solution:

By given the speed of the stream is 3 km/hr

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

Hence,

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

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

We know that,

Distance = Speed × Time

Hence by the first case given,

Distance = (x + 3) × 15

Distance = 15x + 45-------(1)

By the second case given,

Distance = (x - 3) × 20

Distance = 20x - 60----(2)

In equations 1 and 2, the distance travelled is same. Therefore,

20x - 60 = 15x + 45

20x - 15x = 45 + 60

5x = 105

x = 21

Hence speed of the steamer is 21 km/hr.

Now substitute the value of x in equation 1,

Distance = 15x + 45

Distance = 15 × 21 + 45

Distance = 315 + 45

Distance = 360 km

Hence the distance between the towns is 360 km.

Answer 2

$\huge{\boxed{\rm{Question}}}$

A steamer, going downstream in a river, covers the distance between two towns 15 hours. Coming back upstream, it covers this distance in 20 hours. The speed the water is 3 km/hr. Find the distance between two towns.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• A steamer, going downstream in a river, covers the distance between two towns
• 15 hours.

• Coming back upstream, it covers this distance in 20 hours.

• The speed of the water is 3 km/hr.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Distance between two towns.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Distance between two towns = 360 kilometres.

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that a steamer, going downstream in a river, covers the distance between two towns 15 hours. Coming back upstream, it covers this distance in 20 hours. The speed the water is 3 km/hr. Afterthat it ask us to find the distance between two towns.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question we have to learn the formula to find Distance. After that as we take some assumptions. According to this assumptions we have to put the values and we get Eǫᴜᴀᴛɪᴏɴ ❶ and Eǫᴜᴀᴛɪᴏɴ ❷. Now we get the speed of steamer = 21 km/h .After that substituting the values we gt our final result that is 360 km/hr

According to the question we know that,

• The steam's speed is given = 3 km/h

Afterthat,

• Let the steamer's speed as x km/h

So,

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

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

Now to solve this question we have to use the formula to find Distance and it's Distance = Speed × Time.

Lets start solving the question !

According to 1st case we get the following results –

• Distance = (x+3) × 15

• Distance = 15x + 45 Eǫᴜᴀᴛɪᴏɴ ❶

According to 2nd case we get the following results –

• Distance = (x-3) × 20

• Distance = 20x - 60 Eǫᴜᴀᴛɪᴏɴ ❷

Substituting the values of Eǫᴜᴀᴛɪᴏɴ ❶ and Eǫᴜᴀᴛɪᴏɴ ❷ we get –

• Distance = 20x - 60 = 15x + 45

• Distance = 20x - 15x = 45 + 60

• Distance = 5x = 105

• Distance = x = 105/5

• Distance = x = 21

Hence, speed of steamer is 21 km/hr.

Now substituting the value of x in Eǫᴜᴀᴛɪᴏɴ ❶

• Distance = 15x + 45

• Distance = 15 × 21 + 45

• Distance = 315 + 45

• Distance = 360

The distance between two towns is 360 km/h.