Explanation

Let's say the person's usual travel time to his office is x minutes.

Since he is walking at 5/6 of his usual speed, his new speed is 5/6 of his usual speed.

The time taken to cover the same distance at this new speed is 6/5 of his usual time (since speed and time are inversely proportional).

So, the new time taken = (6/5)x

Since he is 40 minutes late, the new time taken is 40 minutes more than his usual time:

(6/5)x = x + 40

Simplifying the equation:

(1/5)x = 40

x = 200 minutes

Converting x to hours and minutes:

x = 3 hours 20 minutes

Explanation

Explanation

To find the power of the combination of lenses, we can use the formula:

P_total = P1 + P2

Where:

- P_total is the total power of the combination

- P1 is the power of the convex lens

- P2 is the power of the concave lens

The power of a lens is given by the formula:

P = 1 / f

Where:

- P is the power of the lens

- f is the focal length of the lens

Given that the focal length of the convex lens is 40 cm and the focal length of the concave lens is -25 cm (negative because it is concave), we can calculate their respective powers:

P1 = 1 / 40 cm = 0.025 dioptres (approximately)

P2 = 1 / -25 cm = -0.04 dioptres (approximately)

Now, we can calculate the total power of the combination:

P_total = P1 + P2

= 0.025 dioptres + (-0.04 dioptres)

= -0.015 dioptres / -1.5  (approximately)

(0.015 = 1.5= 0.015 * 100= 1.5)

Explanation

This problem involves a proportional relationship between machines, work, and time.

We are told that:

• 5 machines do 5 works in 5 minutes.

The rate at which each machine works is:

Rate of 1 machine= 5 works/ 5machines×5minutes= 1 works / 5minutes​

So, 1 machine can complete 1 work in 5 minutes.

Explanation

96 kilometers to meters:
$1 , text{km} = 1000 , text{meters}$
$96 , text{km} times 1000 = 96,000 , text{meters}$
Answer: 96,000 meters

Explanation

Speed of the boat in standing water = 14 kmph

Speed of the stream = 1.2 kmph

Speed downstream = 14 + 1.2 = 15.2 kmph

Speed upstream = 14 - 1.2 = 12.8 kmph

Distance to the place = 4864 km (same for downstream and upstream)

Time taken downstream:

Time = Distance / Speed

= 4864 / 15.2

= 320 hours

Time taken upstream:

Time = Distance / Speed

= 4864 / 12.8

= 380 hours

Total time taken:

Total Time = Time downstream + Time upstream

= 320 + 380

= 700 hours

Explanation

To convert minutes to seconds:

1 minute = 60 seconds

120 messages/minute = 120 messages/60 seconds

= 2 messages/second

For 150 seconds:

2 messages/second * 150 seconds = 300 messages

Explanation

When boiling multiple eggs together, the cooking time doesn't increase linearly with the number of eggs. 

As long as the eggs are not stacked on top of each other and are fully submerged in water, the cooking time remains roughly the same.

So, it will still take 2 minutes to boil 5 eggs together!

Explanation

To solve this problem, we need to convert the speed from km/hr to m/s and then use the formula:

Time = Distance / Speed

First, let's convert the speed:

63 km/hr = 63 x (1000 m / 3600 s) = 17.5 m/s

Now, let's calculate the time:

Time = Distance / Speed

= 250 m / 17.5 m/s

= 14.3 seconds

Explanation

To find the period and wavelength of a wave, we can use the formulas:

Period (T) = 1 / Frequency (f)

Wavelength (λ) = Speed (v) / Frequency (f)

Given:

Frequency (f) = 2.5 Hz

Speed (v) = 1.5 m/s

Step 1: Calculate the period (T):

Using the formula, T = 1 / f, we can substitute the given frequency to find the period:

T = 1 / 2.5 Hz

T = 0.4 s

Therefore, the period of the wave is 0.4 seconds.

Step 2: Calculate the wavelength (λ):

Using the formula, λ = v / f, we can substitute the given speed and frequency to find the wavelength:

λ = 1.5 m/s / 2.5 Hz

λ = 0.6 m

Therefore, the wavelength of the wave is 0.6 meters.

In summary, the wave has a period of 0.4 seconds and a wavelength of 0.6 meters.