Explanation

When two objects are moving towards each other, their relative speed is the sum of their individual speeds.

• Speed of the first train = 60 km/h
• Speed of the second train = 40 km/h
• Distance between them = 150 km

The relative speed is:

$$60 , text{km/h} + 40 , text{km/h} = 100 , text{km/h}$$

Now, to find the time it takes for the trains to meet, use the formula:

$$text{Time} = frac{text{Distance}}{text{Relative Speed}}$$ $$$$Time=150 km100 km/h=1.5 hours=1 hour 30 minutestext{Time} = frac{150 , text{km}}{100 , text{km/h}} = 1.5 , text{hours} = 1 , text{hour} , 30 , text{minutes}Time=150km/100km​/h=1.5hours=1hour30minutes

Explanation

Track length = 1 km

Formula used:

Distance Speed x Time

Calculation:

"A" beats "B" by 50 m or 10 sec, means "B" covers 50 m in 10 sec

Speed of "B" = 50/10 = 5 m/s

Time to cover 1000 m = 1000/5 = 200 sec

"A" beats "B" by 10 sec means

"A" reach 10 sec early

Time taken by "A" to complete the race = 200 - 10 = 190 sec

∴ Time taken by "A" to complete the race is 190 sec.

Explanation

Length of the train = 240 m

Time taken to pass the pole = 24 seconds

Speed of the train = Distance / Time = 240 m / 24 s = 10 m/s

Total distance to be covered = Length of train + Length of platform = 240 m + 650 m = 890 m

Time taken to pass the platform = Total distance / Speed = 890 m / 10 m/s = 89 seconds

Explanation

Volume of tank = 200 m x 150 m x 2 m = 60,000 m³

Volume of water flowing per second = (1.5 m x 1.25 m) x (20 km/h x (1000/3600)) = 208.33/9 m³/s

Time taken to fill the tank = 60,000 m³ / (208.33/9 m³/s) = 2600 seconds

Convert seconds to minutes = 2600 s / 60 = 43.33 minutes

Time taken to fill 2 meters = 43.33 x (2/3) = 96 minutes

Explanation

Given Information:

- Total students = 100

- Students playing football = 60

- Students playing cricket = 55

- Students not playing any game = 5

Calculation Steps:

1. Calculate the number of students playing at least one game:

2. = 100 - 5 = 95

2. Use the inclusion-exclusion principle:

  95 = 60 + 55 - x

   Simplifying this gives:

   95 = 115 - x implies x = 115 - 95 = 20

Explanation

Explanation

To find the total distance traveled, you need to convert the time from hours and minutes to just hours. There are 60 minutes in an hour, so:

24 minutes = 24/60 = 0.4 hours

Adding this to the 3 hours, you get:

3 hours + 0.4 hours = 3.4 hours

Now, you can multiply the total hours by the average speed (35 miles per hour) to get the total distance:

3.4 hours x 35 miles/hour = 119 miles

So, the correct answer is 119 miles.

Explanation

Convert the race distance from 1 km to meters: 1 km = 1000 m

Find the distance covered by X in the race: 48 m (given)

Find the distance covered by Y in the race: 42 m (given)

Since X beats Y, X covers the entire race distance (1000 m), while Y covers a shorter distance.

To find the distance by which X beats Y, subtract the distance covered by Y from the race distance: 1000 m - 42 m x (1000/48) = 1000 - 875 = 125 m

So, X beats Y by 125 meters.

Explanation

Let the speed of the train be x km/h and the speed of the car be y km/h.

Case 1: He travels 120 km by train and the rest (480 km) by car, taking 8 hours in total.

Time taken by train = Distance / Speed = 120 km / x km/h = 120/x hours

Time taken by car = Distance / Speed = 480 km / y km/h = 480/y hours

Total time = 8 hours = (120/x) + (480/y)

Case 2: He travels 200 km by train and the rest (400 km) by car, taking 8 hours 20 minutes (or 8.33 hours) in total.

Time taken by train = Distance / Speed = 200 km / x km/h = 200/x hours

Time taken by car = Distance / Speed = 400 km / y km/h = 400/y hours

Total time = 8.33 hours = (200/x) + (400/y)

Now, we have two equations and two variables. Solving them simultaneously, we get:

x = 60 km/h (speed of the train)

y = 80 km/h (speed of the car)

Explanation

Step 1: Use the Diagonal Formula for a Square

For a square with side length $s$, the diagonal $d$ is given by:

Substituting $d = 30$

$sqrt{2} approx 1.414$

Step 3: Calculate the Perimeter

The perimeter $P$ of a square is: