Idea of Speed, Distance & Time — Statement I-II Type Questions

Statement 1 : A boy covers a distance of 15 km in 2 min and next 15 km in 3 min. The speed of the boy is uniform.

Statement 2 : Since total distance covered = 30 km and total time taken = 5 min ∴ Average speed of the boy = 6 km/min

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

The boy covers the first 15 km in 2 min and the next 15 km in 3 min.

For a uniform speed, equal distances must be covered in equal intervals of time. Here equal distances (15 km each) are covered in different times (2 min and 3 min), so the speed is not uniform, it is variable.

So, Statement 1 is false.

Total distance covered = 15 km + 15 km = 30 km.

Total time taken = 2 min + 3 min = 5 min.

Average speed = $\dfrac{\text{Total distance covered}}{\text{Total time taken}} = \dfrac{30}{5} = 6$ km/min.

So, Statement 2 is true.

Hence, option 4 is the correct option.

Statement 1 : Mr. John covers a certain distance between two places in 2 hr 30 min with the uniform speed of 60 km/hr. The distance between the two places = 60 × 150 km.

Statement 2 : Distance covered = Speed × time = 60 × 150 km

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Given,

Uniform speed = 60 km/hr and time = 2 hr 30 min.

To use Distance = Speed × time, the time must be in hours.

Time = 2 hr 30 min = $2\dfrac{1}{2}$ h = $\dfrac{5}{2}$ h.

∴ Distance = Speed × time = 60 × $\dfrac{5}{2}$ = 150 km, and not 60 × 150 km.

In both statements the time 2 hr 30 min has been wrongly taken as 150 (minutes) instead of $\dfrac{5}{2}$ hours, which gives the incorrect expression 60 × 150 km.

So, Statement 1 is false.

The relation Distance covered = Speed × time is correct, but the substitution 60 × 150 km is wrong, so the value stated in Statement 2 is also incorrect.

So, Statement 2 is false.

Hence, option 2 is the correct option.