MATH SOLVE

4 months ago

Q:
# 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 speed and the time needed to travel 150 km are inversely proportional quantities?I need to know how to explain the last sentence.

Accepted Solution

A:

Answer:Part 1) It took the motorcyclist 2 hours to cover the entire distance.Part 2) It took the bus 2.5 hours to cover the entire distance.Part 3) It took the truck 3 hours to cover the entire distance.Part 4) It took the bicyclist 7.5 hours to cover the entire distance.Part 5) The explanation in the procedureStep-by-step explanation:we know thatThe speed is the ratio between the distance and the timeLets -----> speed in km/hd ----> distance in kmt ----> the time in hoursso[tex]s=\frac{d}{t}[/tex]Part 1) A distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/hHow much time did each require to travel the entire distance?we have[tex]d=150\ km[/tex][tex]s=75\ km/h[/tex]substitute in the formula and solve for t[tex]75=\frac{150}{t}[/tex][tex]t=\frac{150}{75}[/tex][tex]t=2\ h[/tex]thereforeIt took the motorcyclist 2 hours to cover the entire distance.Part 2) A distance of 150 km was covered by a bus traveling at an average speed of 60 km/hHow much time did each require to travel the entire distance?we have[tex]d=150\ km[/tex][tex]s=60\ km/h[/tex]substitute in the formula and solve for t[tex]60=\frac{150}{t}[/tex][tex]t=\frac{150}{60}[/tex][tex]t=2.5\ h[/tex]thereforeIt took the bus 2.5 hours to cover the entire distance.Part 3) A distance of 150 km was covered by a truck traveling at an average speed of 50 km/hHow much time did each require to travel the entire distance?we have[tex]d=150\ km[/tex][tex]s=50\ km/h[/tex]substitute in the formula and solve for t[tex]50=\frac{150}{t}[/tex][tex]t=\frac{150}{50}[/tex][tex]t=3\ h[/tex]thereforeIt took the truck 3 hours to cover the entire distance.Part 4) A distance of 150 km was covered by a bicyclist traveling at an average speed of 20 km/hHow much time did each require to travel the entire distance?we have[tex]d=150\ km[/tex][tex]s=20\ km/h[/tex]substitute in the formula and solve for t[tex]20=\frac{150}{t}[/tex][tex]t=\frac{150}{20}[/tex][tex]y=7.5\ h[/tex]thereforeIt took the bicyclist 7.5 hours to cover the entire distance.Part 5) Explain why speed and the time needed to travel 150 km are inversely proportional quantities?we know thatA relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]In this problemthe constant k will be the distance dthe variable y will be the speed sthe variable x will be the time tsospeed and time are inversely proportional quantities becausewhen speed increases -------> the time decreaseswhen speed decreases -------> the time increases