Two runners cover the same distance at the speeds of 15 km/h and 16 km/h respectively. Find the distance travelled when one takes 16 min longer than the other.

Correct option is B

Given:

​The first runner runs at a speed of 15 km/h.

The second runner runs at a speed of 16 km/h.

The first runner takes 16 minutes longer than the second runner to cover the same distance.

Distance = ?

Formula Used:

​$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$​​

Solution:

Let the distance traveled by both runners be denoted by $D$ kilometers.

Time taken by the first runner (speed 15 km/h) is:

​$$T_1 = \frac{D}{15}$$ 

Time taken by the second runner (speed 16 km/h) is:

$$T_2 = \frac{D}{16}$$ 

​Therefore, the time difference between the two runners is:

​$$T_1 - T_2 = \frac{16}{60} = \frac{4}{15} \text{ hours}$$  

Substitute the values of $$T_1$$ and $$T_2$$​ into this equation:

​$$\frac{D}{15} - \frac{D}{16} = \frac{4}{15}$$ 

​$$\frac{16D-15D}{240} = \frac{4}{15}$$ 

$$\frac{D}{240} = \frac{4}{15}$$ 

​$$D = \frac{4}{15} \times 240$$ 

D = 64 km

The distance traveled by both runners is 64 kilometers.​

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