Question

A swimmer swims 90m long pool . he covers the distance of 180m by swimming from one end to other end back along the same path . If he covers the first 90m at speed of 2m/s, then how fast he swim so that his average speed is 3m/s ?

Answer 1

Given,

 Length of the pool = 90m

Speed to cover first 90 m = 2 m/s

 Since,

Speed = distance / time or Time = distance / speed

Time taken to cover first 90 m = 90 / 2 = 45 sec

Time taken to travel the next 90 m back = t₂

Total distance = 180 m

Therefore,

Total time to cover 180 m = 45 + t₂

Average speed to travel 180 m = 3 m/s

or Average speed = Total distance covered / Total time taken or 3 m/s = 180 / 45 + t₂

By cross multiplication, we get the following result 3* (45 +t₂) = 180 or t2= 15

Hence , time taken to travel back 90 m = 15 sec

To cover his average speed is 3m/s ?

Speed = distance / time = 90 / 15 = 6 m/ s

Hence , he must swim with a speed of 6 sec to make his average speed to be 3 m/s

Answer 2

Answer:

let the time from one end to other= t1

distance from one end to other= 90m

speed= 2m/s

t1= 90/2=45 sec.

let the remaining time be t2

remaining distance= 90m

remaining time= t2

total distance= 180m

total time= 180s + t2

180/45+t2= 3m/s

45+t2= 180/3

45=t2= 60

t2= 60 - 45

= 15 sec

speed required= 90/15

= 6m/s