Arithmetic

Time, Speed & Distance

Medium

John jogs on track $A$ at $6$ kmph and Mary jogs on track $B$ at $7.5$ kmph. The total length of tracks $A$ and $B$ is $325$ metres. While John makes $9$ rounds of track $A$ , Mary makes $5$ rounds of track $B$ . In how many seconds will Mary make one round of track $A$ ?

Entered answer:

✅ Correct Answer: 48

We need to find the lengths of both tracks first, then calculate Mary's time on track A.

Let's say:

Length of track A = x metres

Length of track B = y metres

We know: x + y = 325 metres

Here's the crucial understanding: When John makes 9 rounds of track A and Mary makes 5 rounds of track B, they take the same amount of time because they're jogging simultaneously.

Time for John to complete 9 rounds = Distance ÷ Speed = $\dfrac{9x}{6}$

Time for Mary to complete 5 rounds = Distance ÷ Speed = $\dfrac{5y}{7.5}$

Since these times are equal:

$\dfrac{9x}{6} = \dfrac{5y}{7.5}$

$9x \times 7.5 = 5y \times 6$

$67.5x = 30y$

$9x = 4y$

Therefore: $\dfrac{x}{y} = \dfrac{4}{9}$

This means x : y = 4 : 9

Since x : y = 4 : 9, we can write:

x = 4k and y = 9k (where k is a constant)

Using x + y = 325:

4k + 9k = 325

13k = 325

k = 25

Therefore:

Length of track A = x = 4 × 25 = 100 metres

Length of track B = y = 9 × 25 = 225 metres

Mary needs to complete 100 metres at 7.5 kmph.

First, we convert speed to m/s:

7.5 kmph = 7.5 × $\dfrac{5}{18}$ m/s = $\dfrac{37.5}{18}$ m/s

To convert km/h to m/s: 1 km = 1000 m, 1 hour = 3600 s

So 1 km/h = $\dfrac{1000}{3600}$ m/s = $\dfrac{5}{18}$ m/s

Time = Distance ÷ Speed

Time = 100 ÷ $\dfrac{37.5}{18}$

Time = 100 × $\dfrac{18}{37.5}$

Time = $\dfrac{1800}{37.5}$

Time = 48 seconds

Mary will take 48 seconds to complete one round of track A.

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John jogs on track $A$ at $6$ kmph and Mary jogs on track $B$ at $7.5$ kmph. The total length of tracks $A$ and $B$ is $325$ metres. While John makes $9$ rounds of track $A$ , Mary makes $5$ rounds of track $B$ . In how many seconds will Mary make one round of track $A$ ?