Explanation

Total distance covered by both trains = 1160 + 1160 = 2320 meters

Time taken to cross each other = 20 seconds

Relative speed (combined speed of both trains) = Total distance / Time = 2320 / 20 = 116 meters/second

Since both trains have the same speed, the speed of each train = Relative speed / 2 = 116 / 2 = 58 meters/second

Convert meters/second to km/second: 58 / 1000 = 0.058 km/second (approximately)

Convert km/second to km/hour: 0.058 * 3600 = 208.8 km/hour

Explanation

Pipe A and pipe B can fill the tank in 3 hours and 5 hours, then total work = LCM of (3, 5) = 15 unit

Efficiency of pipe A = 15/3 = 5 unit and efficiency of pipe B = 15/5 = 3 unit

From 7 to 8 AM, pipe A alone done 5 unit, work remains (15 - 5) = 10 unit,

Now, pipe A and B together can do it in = 10/(5 + 3) = 10/8 hours = 10/8 × 60 = 75 min

 The required time is 8 AM + 75 min = 9 AM + 15 min = 9 : 15 AM

∴ The correct answer is 9 : 15 AM

Explanation

In the first y hours, the carpenter lays xy bricks.

In the 2y hours thereafter, he lays (x/2)(2y) = xy bricks.

Altogether, that's xy + xy = 2xy bricks.

Explanation

To find the number of lawns completed in 10 hours, we can set up a proportion:

2 hours / 3 lawns = 10 hours / x lawns

We can then cross-multiply and solve for x:

2x = 3 × 10

2x = 30

x = 30/2

x = 15

So, in 10 hours, 15 lawns will be completed.

Explanation

To calculate speed in km/h:

1. Convert the time to hours:
   $20\text{ minutes}=\frac{20}{60}\text{ hours}=\frac{1}{3}\text{ hours}$

2. Use the formula for speed:
   $text{Speed} = frac{text{Distance}}{text{Time}} = frac{16}{frac{1}{3}} = 16 times 3 = 48 , text{km/h}$
   

So, the speed of the train is 48 km/h.

Explanation

Full tank capacity = Distance ÷ Miles per gallon

= 250 miles ÷ 15 miles/gallon

= 16.67 gallons (approximately)

Now, if the car gets 20 miles per gallon, we can calculate the distance it can travel on a full tank:

Distance = Full tank capacity × Miles per gallon

= 16.67 gallons × 20 miles/gallon

= 333.4 miles

Explanation

To find the average speed, use the formula:

Average Speed = Total Distance / Total Time

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Step 1: Total Distance  

= 30 km + 30 km = 60 km

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Step 2: Time taken in each segment

- First 30 km at 40 km/h  

  Time = Distance ÷ Speed = 30 ÷ 40 = 0.75 hours

- Next 30 km at 20 km/h  

  Time = 30 ÷ 20 = 1.5 hours

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Step 3: Total Time  

= 0.75 + 1.5 = 2.25 hours

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Step 4: Average Speed  

= Total Distance ÷ Total Time = 60 ÷ 2.25 = 26.67 km/h

Explanation

From 10:15 AM to 2:30 PM:

• From 10:15 AM to 2:15 PM is 4 hours.
• From 2:15 PM to 2:30 PM is an additional 15 minutes.

Thus, the total time is 4 hours 15 minutes.

Explanation

The scale is 1 cm : 50 km.

For a distance of 200 km, the map distance is 200 / 50 = 4 cm.

Explanation

To find the speed of the bus, we can use the formula:

Speed = Distance / Time

Plugging in the values given:

Speed = 120 km / 3 hr

Speed = 40 km/hr