Speed, Time & Distance — Mental Maths

Fill in the blanks:

(i) 12 m/sec = ...... km/hr

(ii) 27 km/hr = ...... m/sec.

(iii) At a speed of 54 km/hr, a car will cover a distance of 600 m in ...... seconds.

(iv) At a speed of 45 km/hr, the distance covered in 18 seconds is ...... m.

(v) At a speed of 5 m/s, a distance of 27 km will be covered in ...... hr ...... min.

Answer

(i) To convert a speed of m/sec into km/hr, we multiply by $\dfrac{18}{5}$.

$\Rightarrow 12 \text{ m/sec }= \left(12 \times \dfrac{18}{5}\right) \text{ km/hr }\\[1em] = \dfrac{216}{5} \text{ km/hr }\\[1em] = 43\dfrac{1}{5} \text{ km/hr } = 43.2 \text{ km/hr }$

Hence, 12 m/sec = 43.2 km/hr.

(ii) To convert a speed of km/hr into m/sec, we multiply by $\dfrac{5}{18}$.

$\Rightarrow 27 \text{ km/hr }= \left(27 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{135}{18} \text{ m/sec }\\[1em] = \dfrac{15}{2} \text{ m/sec } = 7.5 \text{ m/sec }$

Hence, 27 km/hr = 7.5 m/sec.

(iii) Given,

Speed = 54 km/hr and distance = 600 m

Converting the speed into m/sec :

$54 \text{ km/hr }= \left(54 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{270}{18} \text{ m/sec }\\[1em] = 15 \text{ m/sec }$

By formula,

$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{600 \text{ m}}{15 \text{ m/sec}}\\[1em] = 40 \text{ seconds }$

Hence, at a speed of 54 km/hr, a car will cover a distance of 600 m in 40 seconds.

(iv) Given,

Speed = 45 km/hr and time taken = 18 seconds

Converting the speed into m/sec :

$45 \text{ km/hr }= \left(45 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{225}{18} \text{ m/sec }\\[1em] = 12.5 \text{ m/sec }$

By formula,

$\text{Distance} = \text{Speed} \times \text{Time}\\[1em] = 12.5 \times 18 \text{ m }\\[1em] = 225 \text{ m }$

Hence, at a speed of 45 km/hr, the distance covered in 18 seconds is 225 m.

(v) Given,

Speed = 5 m/s and distance = 27 km

Converting the speed into km/hr :

$5 \text{ m/s }= \left(5 \times \dfrac{18}{5}\right) \text{ km/hr }\\[1em] = \dfrac{90}{5} \text{ km/hr }\\[1em] = 18 \text{ km/hr }$

By formula,

$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{27 \text{ km}}{18 \text{ km/hr}}\\[1em] = \dfrac{3}{2} \text{ hrs } = 1\dfrac{1}{2} \text{ hrs }\\[1em] = 1 \text{ hr } 30 \text{ min }$

Hence, at a speed of 5 m/s, a distance of 27 km will be covered in 1 hr 30 min.

Write (T) for true and (F) for false for each of the following statements:

(i) Distance = (Speed × Time)

(ii) Speed = (Distance × Time)

(iii) 90 km/hr = 25 m/s

(iv) $12\dfrac{1}{2}$ km/hr = 54 km/hr

(v) A man runs at 18 km/hr. Time taken by him to cover 600 m is 3 minutes.

Answer

(i) Since, Speed = $\dfrac{\text{Distance}}{\text{Time}}$, we get Distance = (Speed × Time).

Hence, the statement is true (T).

(ii) Speed = $\dfrac{\text{Distance}}{\text{Time}}$ and not (Distance × Time).

Hence, the statement is false (F).

(iii) 90 km/hr = $\left(90 \times \dfrac{5}{18}\right)$ m/s = 25 m/s

Hence, the statement is true (T).

(iv) $12\dfrac{1}{2}$ km/hr = 12.5 km/hr, which is not equal to 54 km/hr.

Hence, the statement is false (F).

(v) Given,

Speed = 18 km/hr and distance = 600 m

Converting the speed into m/sec :

18 km/hr = $\left(18 \times \dfrac{5}{18}\right)$ m/s = 5 m/s

By formula,

$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{600 \text{ m}}{5 \text{ m/s}}\\[1em] = 120 \text{ sec }\\[1em] = 2 \text{ minutes }$

Time taken by him to cover 600 m is 2 minutes and not 3 minutes.

Hence, the statement is false (F).