Question

A Park is 1500 metres long and 750
metre wide. A cyclist has to take
four rounds of the park. How
much time he will take at the
speed of 4.5 km/h?
​

Answer 1

Understanding the Question :-

Here it is given that A park is 1500 m long and 750 m wide means it is Rectangular Park whose length and Breadth are 1500 m and 750 m respectively. A cyclist is cycling four rounds around the park at speed of 4.5 km/h. We need to find time taken to complete all four rounds.

Given :-

• Length of Park = 1500 m
• Breadth of Park = 750 m
• Speed of Cyclist = 4.5 km/h.

To find :-

• Time taken to complete.

Concept :-

• Here the concept of relation of speed, time, distance and Perimeter of Rectangle will be used. Also converting meter into Kilometers will be used.

Formula Applies :-

❶ Conversion of Meter to Kilometers

${\boxed{\sf{ No. \: of \: Kilometers = \frac{Number \: of \: Meters \: given}{1000} }}}$

❷ Perimeter of Rectangle

${\boxed{\sf{Perimeter = 2(Length + Breadth) }}}$

❸ Formula of Speed

${\boxed{\sf{Speed = \frac{ Distance }{Time} }}}$

Solution :-

✪ Converting all units of meter into Kilometers :-

Length of Rectangular Park is :

${\sf{\implies{ Length = \dfrac{ No. \: of \: meter }{1000}}}}$

${\sf{\implies{ Length = \dfrac{ 1500 }{1000}}}}$

${\sf{\implies{ Length = \dfrac{ 15 }{10}}}}$

${\sf{\implies{ \underline{ Length = 1.5 \: km}}}}$

Breadth of the Park is :

${\sf{\implies{ Breadth = \dfrac{ No. \: of \: meters }{1000}}}}$

${\sf{\implies{ Breadth = \dfrac{ 750 }{1000}}}}$

${\sf{\implies{ Breadth = \dfrac{ 75}{100}}}}$

${\sf{\implies{ \underline{ Breadth = 0.75 \: km}}}}$

✪ Perimeter of the Rectangular Park is :-

${\sf{\implies{Perimeter = 2(L + B) }}}$

${\sf{\implies{Perimeter = 2(1.5+ 0.75) }}}$

${\sf{\implies{Perimeter = 2(2.25) }}}$

${ \boxed{ \sf{ \implies{Perimeter = 4.5 \: km }}}}$

✪ Distance completed by Cyclist after completing 4 rounds is

${\sf{\implies{Distance = Perimeter \: of \: Rectangular \: field \times 4 }}}$

${\sf{\implies{Distance = 4.5 \times 4 }}}$

$\boxed{\sf{\implies{Distance = 18 \: km }}}$

✪ Time taken to complete 4 rounds is

${\large{\sf{\implies{Speed = \dfrac{ Distance }{Time }}}}}$

Here

• Distance = 18 km
• Speed = 4.5 km/h

Substituting the values.

${\large{\sf{\implies{4.5= \dfrac{ 18 }{Time }}}}}$

${\large{\sf{\implies{Time = \dfrac{ 18 }{4.5}}}}}$

$\large{\underline{\overline{ \boxed {\red{\bf{\implies Time = 4 \: \: h ours }}}}}}$

So, Cyclist will take 4 hours to complete 4 rounds.