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 speed and the time needed to travel 150 km are inversely proportional quantities?

Answer 1

Step-by-step explanation:

Given:

• Distance covered = 150 km
• Speed of the motorcyclist = 75km/hr
• Speed of the bus = 60km/hr
• Speed of the truck = 50km/hr
• Speed of the bicyclist = 20km/hr

To Find:

• Time taken by motorcyclist
• Time taken by bus
• Time taken by truck
• Time taken by bicyclist

Solution:

Time taken by motorcyclist:

→ Time is given by the equation

   Time = Distance/ Speed

→ Substituting the given datas, we get

   Time = 150/75

   $\boxed{Time\:taken\:=\:2\:hours}$

Time taken by bus:

→ Substituting the given datas, in the equation for time, we get

→ Time = 150/60

   $\boxed{Time\:taken\:=\:2.5\:hours}$

Time taken by truck:

→ Substitute the given datas in equation for time

→ Time = 150/50

   $\boxed{Time\:taken\:=\:3\:hours}$

Time take by bicyclist:

→ Substituting the datas in the equation for time

→ Time = 150/20

   $\boxed{Time\:taken\:=\:7.5\:hours}$

→ Here distance is constant

  The equation for speed is given by

  $Speed\:=\:\frac{Distance}{Time}$

  Since distance is a constant,

  Speed ∝ $\frac{1}{Time}$

→ Hence when speed increases, time decreases and vice versa.

Notes:

• Speed is defined as the distance travelled by a body per unit time.
• Speed is a scalar quantity, that is it has only magnitude and no direction.

• $Speed\:=\:\frac{Distance}{Time}$