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

Let's break down the problem to determine if the total time taken is indeed 5 1/2 hours.

Step 1: Determine how many forms are left after the first half-hour

Explanation

Explanation

To determine how many items the machine will produce in 10 minutes:

1. It takes 1/3 minute to produce one item.
2. In 1 minute, the machine produces 3 items (since 1 ÷ 1/3 = 3).
3. In 10 minutes, the machine will produce 3 × 10 = 30 items.

So, the machine will produce 30 items in 10 minutes.

Explanation

To solve the problem, follow these steps:

1: Determine B's efficiency compared to A:

• A can finish the work in 40 days, so A's work rate is  1/40 of the work per day.
  
• If B is 255% less efficient than A, it means B's efficiency is reduced by 255%, which implies B is not practically effective (usually considered inefficient or not working effectively in real terms).

2: Calculate B's efficiency:

• If B is 255% less efficient, B's effective efficiency would be negative, which isn't practically feasible. To make sense of this:
• Assume B’s efficiency is effectively lower compared to A in realistic scenarios.

3: Adjust B's effective efficiency for practical calculations:

• Let's use a model where B is significantly less efficient but not zero. For instance, if B’s efficiency is assumed to be around 10% of A’s for simplicity:
• B can do the work in approximately 400 days.

The closest feasible answer given practical scenarios and combined work rate calculations is None.

Explanation

Let's break this problem down step by step:

1. Let the distance between home and school be x km.
2. Time taken to go to school = Distance / Speed = x / 3
3. Time taken to return home = Distance / Speed = x / 2
4. Total time = 5 hours, so we can set up the equation: x / 3 + x / 2 = 5
5. To solve for x, we can find a common denominator (6) and add the fractions: (2x + 3x) / 6 = 5
6. Combine like terms: 5x / 6 = 5
7. Multiply both sides by 6 to eliminate the fraction: 5x = 30
8. Divide both sides by 5 to solve for x: x = 6

So, the correct answer is: 6 km

Explanation

Time = Distance / Speed

Time = 15 km / 80 kmph = 0.1875 hours

Multiply by 60 to convert to minutes:

0.1875 x 60 = 11.25 minutes

Now, find the time at 60 kmph:

Time = 15 km / 60 kmph = 0.25 hours

Multiply by 60 to convert to minutes:

0.25 x 60 = 15 minutes

Answer: 15 minutes

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

Since there are 8 mango trees, and the distance between each tree is 3 meters, the total distance between the first tree and the eighth tree would be:

7 gaps (between 8 trees) x 3 meters per gap = 21 meters

So, the distance between the first tree and the eighth tree is 21 meters!

Explanation

The logic is:

10 cats can catch 10 rats in 10 seconds

To catch 100 rats, the same 10 cats will take 100 seconds (since the rate of catching rats is the same)

Therefore, the number of cats required remains the same, i.e., 10

So, 10 cats can catch 100 rats in 100 seconds!