a cyclist cycles for 't' sec at a speed of 3m/s and then for the same time at a speed of 5m/s along a straight line due north. what is the average speed of the cyclist.

now, we know that

Solution: 

We know that,

Average Speed = total distance travelled / Total time taken

Now the distance travelled by the cyclist in the first t secs

s1 = 3xt

similarly, the distance travelled by the cyclist in last t secs

s2 = 5xt

so, total distance travelled

s = s1 + s2 = 3t + 5t = 8t

total time taken = t + t = 2t

so, average velocity will be

v = 8t/2t

or v = 4 m/s