T & J travel from Bedk to Jrong, distance of 34km. T is moving at 1/2 km h faster than J and it took T half an hour earlier to Jrong. Speed of T?

The distance between Bedk and Jrong is 34
km.

Let the speed of J be S k/h. Then the speed of T is
(S+1/2) k/h

Now, Let the time needed for J be X hours.
Then, the time needed for T is (X- 1/2) hours.

Now we know
that:

Distance = speed *
Time

==> J's distance = 34 =
S*x

==> T's distance = 34= (S+1/2)*
(X-1/2)

==> s =
34/x

==> s+ 1/2 =
34/(x-1/2)

==> 34/x + 1/2 =
34/(x-1/2)

==> (68 + x)/2x =
34/(x-1/2)

==> (68 + x)/2x =
68/(2x-1)

==> (2x-1)(x+68) =
2x*68

==> (2x^2 + 136x - x - 68 =
136x

==> 2x^2 - x - 68 =
0

Now we will use the quadratic formula to find
x.

==> x1= (1 + sqrt(1+4*2*68)/ 2*2 = (1+ 23.35)/ 4
= 24.35/4

==> x1=
6.08

Then the time needed for J is x = 6.08
hours

==> S= 34/ 6.08= 5.59 km per
hour

==> Then the speed needed for T
is S+ 1/2 = 5.59 + 0.5  = 6.08 km per hour.