Question

Mahmoud runs to a marker and back in 15 minutes. His speed on the way to the marker is 5m/s and his speed on the way back is 4m/s. Find the distance to the marker?

Answer 1

Given:

Mahmoud runs to a marker and back in 15 minutes

His speed on the way to the marker = 5 m/s

His speed on the way back = 4 m/s

To find:

The distance to the marker

Solution:

Time taken by Mahmoud for the entire journey = 15 min = 15×60 = 900 s

Let "x" meter be the distance covered by Mahmoud on the way to the marker

We have the formula:

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

It is given that Mahmoud goes to the marker with a speed of 5 m/s  and then he covers the same distance on his way back with a speed of 4 m/s.

So, we can form an equation as,

[Time taken to run to the marker] + [Time taken to run back] = [Total time of the journey]

⇒ $\frac{x}{5} \:+\: \frac{x}{4} = 900$

⇒ $\frac{4x\:+\:5x}{20} = 900$

⇒ $\frac{9x}{20} = 900$

⇒ $9x = 900 \times 20$

⇒ $x = \frac{18000}{9}$

⇒ $x = 2000 \:m$ or $2\:km$

Thus, the distance to the marker is 2000 m or 2 km.

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