an airplane travels 990 kilometers in the same time that a ship travels 120 kilometers. If the airplane is 10kph more than 8 times the rate of the ship, what is the rate of each?
Answer (2)
Answer:Step-by-step explanation:
Answer:Ship: 40 km/h, Airplane: 330 km/hStep-by-step explanation:1. **Define Variables:** - Let \( v_s \) be the speed of the ship in km/h. - Let \( v_a \) be the speed of the airplane in km/h.2. **Set Up the Relationships:** - The airplane travels 990 km, and the ship travels 120 km in the same time. - The time taken by both is equal, so: \[ \frac{990}{v_a} = \frac{120}{v_s} \] - The airplane's speed is 10 km/h more than 8 times the speed of the ship: \[ v_a = 8v_s + 10 \]3. **Solve for \( v_s \) and \( v_a \):** First, express the time equality in terms of \( v_s \): \[ \frac{990}{8v_s + 10} = \frac{120}{v_s} \] Cross-multiply to clear the fractions: \[ 990 \cdot v_s = 120 \cdot (8v_s + 10) \] \[ 990v_s = 960v_s + 1200 \] Solve for \( v_s \): \[ 990v_s - 960v_s = 1200 \] \[ 30v_s = 1200 \] \[ v_s = \frac{1200}{30} = 40 \text{ km/h} \] Now, substitute \( v_s = 40 \) into the airplane's speed equation: \[ v_a = 8 \cdot 40 + 10 = 320 + 10 = 330 \text{ km/h} \]4. **Conclusion:** - The rate of the ship is 40 km/h. - The rate of the airplane is 330 km/h.
