Travel Speed | MCQs

Explanation

1. Let Ali's speed be x kmph. Then, the time taken by Ali to cover 30 km is 30/x hours.

2. Since Ali takes 2 hours more than Raza, the time taken by Raza to cover 30 km is (30/x) - 2 hours.

3. If Ali doubles his speed, his new speed is 2x kmph. The time taken by Ali to cover 30 km at this new speed is 30/(2x) hours.

4. According to the problem, if Ali doubles his speed, he would take 1 hour less than Raza. So, we can set up the equation:

(30/x) - 2 = (30/(2x)) - 1

Simplifying the equation, we get:

30/x - 2 = 15/x - 1

Multiplying both sides by x, we get:

30 - 2x = 15 - x

Simplifying further, we get:

x = 5

So, Ali's speed is 5 kmph.

Explanation

Let the total distance be x km.

The man covers half the distance at 6 km/hr, so the time taken to cover this half is:

Time = Distance / Speed = (x/2) / 6 = x/12

The man covers the remaining half at 3 km/hr, so the time taken to cover this half is:

Time = Distance / Speed = (x/2) / 3 = x/6

The total time taken to cover the entire distance is the sum of the times taken to cover each half:

Total Time = x/12 + x/6

To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as:

Total Time = x/12 + 2x/12 = 3x/12 = x/4

Now, we can find the average speed:

Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr

So, the correct answer is: 4 km/hr

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