Respuesta :
Answer:
(a) Cyclist A travels faster.
(b) The time taken by cyclists A and B is 10 minutes and 8.58 minutes respectively.
Explanation:
Given that the speed of cyclist A= 24 km/h
As 1 km = 1000 m and 1 hour= 3600 seconds.
So, [tex]24 \frac {km}{h}=24\times \frac{1000 m}{3600 s}=\frac{20}{3}\frac {m}{s}=6.67 m/s[/tex]
and the speed of cyclist B = 6.8 m/s.
The length of the road = 4 km=4000 m.
(a) Speed of cyclist A is 6.67 m/s which is more than the 6.8 m/s.
Hence, cyclist A travels faster.
(b) If d be the distance to be traveled and V be the speed, than the time, t, required is,
[tex]t=\frac{d}{V}\cdots(i)[/tex]
For cyclist A:
As A is located at the beginning of the road, he has to cover full length of the road.
So, the distance to be covered by cyclist A =4 km.
Hence, from equation (i), the time taken by cyclist A is
[tex]t=\frac{4}{24}=\frac{1}{6}[/tex] hour
[tex]=\frac{1}{6}\times {60}=10[/tex] minutes. [ as 1 hour = 60 minumes]
So, time taken by cyclist A is 10 minutes.
For cyclist B:
As B is located 500 meters later from the beginning of the road, he has to cover the remaining length of the road.
So, the distance to be covered by cyclist B =4000 m-500 m= 3500 m.
Hence, from equation (i), the time taken by cyclist B is
[tex]t=\frac{3500}{6.8}=514.71[/tex] seconds
As 60 seconds= 1 minute.
So, t= 514.71/60 minutes = 8.58 minutes.
[tex]=\frac{1}{6}\times {60}=10[/tex] minutes. [ as 1 hour = 60 minumes]
So, the time taken by cyclist B is 8.58 minutes.
