Mahmoud runs to a marker and back in 15 minutes (900 seconds). His speed on the way to the marker is 5 m/s and his speed on the way back is 4 m/s. We need to find the distance to the marker.

1. Problem Description

Mahmoud runs to a marker and back in 15 minutes (900 seconds). His speed on the way to the marker is 5 m/s and his speed on the way back is 4 m/s. We need to find the distance to the marker.

2. Solution Steps

Let $d$ be the distance to the marker in meters.

The time taken to run to the marker is $t_1 = \frac{d}{5}$ seconds.

The time taken to run back from the marker is $t_2 = \frac{d}{4}$ seconds.

The total time taken is $t_1 + t_2 = 900$ seconds.

So, we have the equation:

$\frac{d}{5} + \frac{d}{4} = 900$

To solve for $d$, we find a common denominator for the fractions, which is

2

0. $\frac{4d}{20} + \frac{5d}{20} = 900$

$\frac{9d}{20} = 900$

Multiply both sides by 20:

$9d = 900 \times 20$

$9d = 18000$

Divide both sides by 9:

$d = \frac{18000}{9}$

$d = 2000$

3. Final Answer

The distance to the marker is 2000 meters.