# Problem Statement A surveyor measures a distance of **300 m** using a chain that is **.1 m too long per 30 m**. Calculate the **actual distance**. --- # Step-by-Step Solution ## 1. Understand the Error - **Measured Length of Chain:** Each "30 m" chain is actually **30.1 m** long (since .1 m too long). - When the surveyor thinks they are measuring 30 m, they are actually measuring 30.1 m. ## 2. Calculate Correction Factor **Correction Factor** = Actual length / Measured length For each 30 m measured, the actual length covered is 30.1 m. So, \[ \text{Actual distance per measured 30 m} = 30.1\ \text{m} \] ## 3. Find How Many Chains Were Used \[ \text{Number of chains laid} = \frac{\text{Measured distance}}{\text{Nominal chain length}} \] \[ = \frac{300\ \text{m}}{30\ \text{m}} = 10 \] ## 4. Calculate Actual Distance Each chain actually measures 30.1 m, so: \[ \text{Actual distance} = \text{Number of chains} \times \text{Actual length of chain} \] \[ = 10 \times 30.1 = 301\ \text{m} \] --- # Final Answer \[ \boxed{301\ \text{m}} \] **The actual distance is 301 m.**