Question

A distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/h, by a bus at 60 km/h, a truck at 50 km/h, and a bicyclist at 20 km/h. How much time did each require to travel the entire distance? Explain why the speed and the time needed to travel 150 km are inversely proportional quantities. for The motorcyclist required hours, the bus required hours, the truck required hours, the bicyclist required hours.

Answer 1

A)

• motorcylcist: 2 hours
• bus: 2.5 hours
• truck: 3 hours
• bicyclist: 7.5 hours

B) It is a matter of definition: speed = distance/time. Speed is proportional to distance and inversely proportional to time.

Explanation:

Speed is defined as the ratio of distance to the time required to cover that distance:

... speed = distance/time

Solving this relation for time, we have ...

... time = distance/speed

a) For each of the modes of transportation, we can find the time by using this relation.

... motorcyle: (150 km)/(75 km/h) = 2 h

... bus: (150 km)/(60 km/h) = 2.5 h

... truck: (150 km)/(50 km/h) = 3 h

... bicycle: (150 km)/(20 km/h) = 7.5 h

b) For a given distance, speed and time are inversely related as a matter of definition.