Question

(a) a spacecraft making a flight near a newly discovered planet traveled 72.6 kilometers (km) in 6 seconds at a constant speed. each kilometer required 5 liters of fuel. the control center would like to explore more of the planet and considers extending the flight to 9 seconds, traveling the same distance each second as last time. fill in the blanks below. then use the diagram to show the distance traveled and fuel used for the 9 second flight. distance traveled each second: \boxed{} km amount of fuel used for each second: \boxed{} liters (diagram: 1 second, 1 second (2 seconds total), km, km, liters, liters) (b) how much fuel would be needed if the spacecraft traveled for 9 seconds? \boxed{} liters

Explanation:

Step1: Find distance per second

The spacecraft travels 72.6 km in 6 seconds. To find the distance per second, divide total distance by time: $\frac{72.6}{6} = 12.1$ km per second.

Step2: Find fuel per second

Each km uses 5 liters, and per second it travels 12.1 km. So fuel per second is $12.1 \times 5 = 60.5$ liters.

Step3: Fuel for 9 seconds (part b)

First, find total distance in 9 seconds: $12.1 \times 9 = 108.9$ km. Then, fuel used is $108.9 \times 5 = 544.5$ liters. (Or, since fuel per second is 60.5, $60.5 \times 9 = 544.5$ liters.)

Answer:

(a) Distance traveled each second: $\boldsymbol{12.1}$ km
Amount of fuel used for each second: $\boldsymbol{60.5}$ liters
(b) Fuel needed for 9 seconds: $\boldsymbol{544.5}$ liters