Question

The distance between two cities is 180 km. The distance was covered by a car at a rate of 50 km/h, by a bus at 45 km/h, by a truck at 49 km/h, and by a bicycle at 25 km/h. How long did each take to travel the entire distance? Are speed and time directly proportional or inversely proportional? What is the constant variation?

A) Car: 3.6 hours, Bus: 4 hours, Truck: 3.67 hours, Bicycle: 7.2 hours; Speed and time are inversely proportional, the constant variation is 180.
B) Car: 3 hours, Bus: 4 hours, Truck: 3.67 hours, Bicycle: 7.2 hours; Speed and time are directly proportional, the constant variation is 4.
C) Car: 3.6 hours, Bus: 4 hours, Truck: 3.67 hours, Bicycle: 7.2 hours; Speed and time are directly proportional, the constant variation is 180.
D) Car: 3 hours, Bus: 4 hours, Truck: 3.67 hours, Bicycle: 7.2 hours; Speed and time are inversely proportional, the constant variation is 4.

Answer 1

The car took 3.6 hours, the bus 4 hours, the truck 3.67 hours, and the bicycle 7.2 hours to cover the distance. Speed and time are inversely proportional, with a constant variation of 180 km.

Step-by-step explanation:

To determine how long it took for each mode of transportation to cover the 180 km between two cities, we use the formula time = distance ÷ speed. We will calculate the time taken for each vehicle and also discuss the relationship between speed and time.

• For the car traveling at 50 km/h: time = 180 km ÷ 50 km/h = 3.6 hours.
• For the bus traveling at 45 km/h: time = 180 km ÷ 45 km/h = 4 hours.
• For the truck traveling at 49 km/h: time = 180 km ÷ 49 km/h = 3.67 hours (rounded to two decimal places).
• For the bicycle traveling at 25 km/h: time = 180 km ÷ 25 km/h = 7.2 hours.

Speed and time are inversely proportional, which means that as the speed increases, the time taken to cover the same distance decreases. This relationship can be expressed by the equation speed × time = constant, where the constant is the distance traveled. In this case, the constant of variation is 180 km, since that is the distance traveled regardless of the speed.

The correct answer is:
A) Car: 3.6 hours, Bus: 4 hours, Truck: 3.67 hours, Bicycle: 7.2 hours; Speed and time are inversely proportional, the constant variation is 180.