Question

A bus runs at 40 km/h to reach its destination but arrives 11 min late. If it runs at
50 km/h, it will be 5 min late. Find the correct time in which the bus will not be late in
reaching its destination​

Answer 1

Answer:

❀ʀᴇǫᴜɪʀᴇᴅ ᴀɴsᴡᴇʀ:

Let the correct time for the train to complete the journey is x minuets

Then train cover distance in x+11 minuets at speed 40 km\hr = $\frac{40(x + 11)}{60} km$

Then train cover distance in x+5 minuets at speed 50 km\hr = $\frac{50(x + 5)}{60} km$

Both are same then $\frac{40(x + 11)}{60} = \frac{50(x + 5}{60}$

∴40x+440=50x+250

∴−10x=−190

∴x=19 minutes

hence the answer is x= 19 minutes

$\sf\blue{hope \: this \: helps \: you!! \: }$

Answer 2

$\large\red\sf{❀ʀᴇǫᴜɪʀᴇᴅ\ ᴀɴsᴡᴇʀ:}$

Answer:

In 19 minutes, the bus will not be late in reaching its destination.

Step-by-step explanation:

This question can be solve by 2 methods.

Given -

A bus runs at 40 km per hour to reach its destination.

The bus arrives 11 mins late.

It runs at 50 km per hour it will be 5 minute late.

To Find

The time in which the bus will not be late in reaching its destination.

Solution 1 -

Consider the -

Time as - t.

It implies,

Increase in speed by 25% will decrease of 1/5th in time if distance is constant.

So,

$\begin{gathered}\sf\\ \\\implies \dfrac{t}{5} = (11- 5) = 6\\ \\\implies t = 30m.\\ \\\end{gathered}$

We get the normal time as 30 minutes. But it is given that the bus arrives 11 mins late.

So,

$\sf \implies 30-11 = 19$

∴ The answer is 19 Minutes.

$\rule{300}{1.5}$

Solution 2 -

Find the Ratio of the speeds & Time.

So,

Ratio of speeds = 40 : 50 = 4 : 5

Now,

If distance is constant then, Time is inversely proportional to Speed.

So,

Time Ratio = 5 : 4

Time saved = $\sf \dfrac{(5 - 4)}{5}=\dfrac{1}{5}$

⇒ 30 minutes.

⇒ 30 - 11 = 19 minutes.

∴ The answer is 19 Minutes.

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