Richa and Ritika cycled a distance on different cycles such that Richa’s speed is 6 km/h more than Ritika’s speed. If the ratio of the time taken by Richa and Ritika to cycle the distance is 3 ∶ 4 then what is the speed of Ritika in m/s?

Richa and Ritika cycled a distance on different cycles such that Richa’s speed is 6 km/h more than Ritika’s speed. If the ratio of the time taken by Richa and Ritika to cycle the distance is 3 ∶ 4 then what is the speed of Ritika in m/s? Correct Answer 5 m/s

Given:

Richa’s speed is 6 km/h more than Ritika’s speed.

The ratio of the time taken by Richa and Ritika = 3 ∶ 4

Concept Used:

The distance travelled or covered by a person or an object in unit time, is called its speed.

The unit of speed is m/s or km/h or kmph.

Formula Used:

S = D/T

where,

S = Speed,

D = Distance Covered,

T = Time Taken

The unit of speed is m/s or km/h or kmph.

Calculation:

Let the speed of Ritika be S, and Time taken by Ritika be T.

So, According to question,

For Ritika,

S × T = D      ---- (1)

And for Richa,

(S + 6) × {(3/4) × T} = D      ---- (2)

From equation (1) and (2),

S × T = (S + 6) × {(3/4) × T}

⇒ S × T = (S + 6) × (3T/4)      (∵ Time taken by Richa ∶ Time taken by Ritika = 3 ∶ 4)

⇒ 4S/3 = S + 6

⇒ 4S/3 – S = 6

⇒ (4S – 3S)/3 = 6

⇒ S = 3 × 6

⇒ S = 18 km/h

Now, Ritika’s speed in m/s = 18 × 1000/3600

⇒ 18 × 5/18

⇒ 5 m/s

∴ Ritika’s speed is 5 m/s.

Important Points

To convert a speed given in km/h to m/s, multiply the speed by 5/18

To convert a speed given in m/s to km/h, multiply the speed by 18/5

Mistake Points

The unit of given speed is km/h but the question is asking the speed in m/s. So, make sure to convert the unit of the answer to the required unit to avoid getting the wrong answer.