Question

A man walking diametrically across a circular grass plot, finds that it has taken him 45 sec. less than if he had kept to the path round the outside. if he walks 90 metres per minute, find the circumference of the grass plot.

Answer 1

Let the diameter of the circle be d

Time taken to reach from A to B diametrically be t

∴ Time taken to reach from A to B while on the circular path =(t+45)s

This path is semicircular

∴ To cover a distance of

2πd

​

the man takes (t+45)s

In 1 min the man covers=80m

∴ \In (t+45)s=

180×(t+45)

= 6080 ×(t+45)s

∴ 2πd= 6080×(t+45)s

Also,

d= 6080t

$$=>d=\dfrac{8}{6}t$$

$$=>t=\dfrac{6d}{8}$$

∴ 2πd= 6080( 86d +45)

$$=>\dfrac{\pi d}{2}=\dfrac{4}{3}(\dfrac{6d+360}{8})$$

$$=>d=\dfrac{7}{22\times 3}(6d+360)$$

$$=>d=\dfrac{7d}{11}+38.18$$

$$=>d=\dfrac{38.18\times 11}{4}$$

$$=>d=104.995$$

$$=>d\simeq 105 m$$