Arithmetic

Time, Speed & Distance

Medium

A and B started together to cover a certain distance, at a speed of 8 km/h and 10 km/h, respectively. If A arrives 15 minutes after B, then find the distance.

8 km

12 km

15 km

10 km

✅ Correct Option: 4

A walks at 8 km/h and B walks at 10 km/h. They start together at the same time and travel to the same destination. A arrives 15 minutes after B.

Let the distance be $d$ km.

Time taken by A = $\frac{d}{8}$ hours

Time taken by B = $\frac{d}{10}$ hours

Since A arrives 15 minutes after B, the time difference is 15 minutes.

Converting to hours: 15 minutes = $\frac{15}{60} = \frac{1}{4}$ hour

The equation becomes:

$\frac{d}{8} - \frac{d}{10} = \frac{1}{4}$

Finding LCM of 8 and 10, which is 40:

$\frac{5d - 4d}{40} = \frac{1}{4}$

$\frac{d}{40} = \frac{1}{4}$

$d = \frac{40}{4}$

$d = 10$

Therefore, the distance is 10 km.

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A and B started together to cover a certain distance, at a speed of 8 km/h and 10 km/h, respectively. If A arrives 15 minutes after B, then find the distance.

Solution

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