(b) Let the speed of faster swimmer be x km/h.
Then, speed of slower swimmer =
×x=x km/h
Now, distance covered by both in 2 h.
Faster swimmer = 2x km
and slower swimmer =
x×2=x km
After, 2 h the distance between them is 100 km.
From the figure,
(OE)2+(OS)2=(ES)2⇒
(x)2+(2x)2=(100)2[Here, S = South direction, E = East direction, O = Origin]
⇒
x2+4x2=10000⇒
=10000⇒
=10000⇒
x2=∴ x =
√ =
= 40 km/h
∴ Speed of faster swimmer = 40 km/h
Direction of faster swimmer can also be taken towards East.