Explanation:

You may solve for D and S by writing the equations as:

Both these equations can be solved quickly to get s = 65 Km/hr, t = 150 hr.
Therefore, D = 9750 Km. I want to reiterate that using the first approach is perfectly fine.
That's how I would do it. It is better to spend 20 seconds extra and get the right answer instead of getting it wrong with something you are not comfortable with.
Alternate Solution:
Let the normal speed be s
and the normal time be t
The distance D = st.
When speed decreases by 15 kmph, time increases by 45 hours. The distance will still be the same.
D = (s-15)(t+45)
st = (s-15)(t+45)
st = st +45s - 15t - 15*45
45s - 15t - 15*45 = 0
3s -t -45 = 0
3s = t + 45
t = 3s - 45
When speed increases by 10 kmph, time decreases by 20 hours. The distance will still be the same.
D = (s+10)(t-20)
st = (s+10)(t-20)
st = st -20s + 10t - 10*20
-20s + 10t - 10*20 = 0
-2s +t -20 = 0
t = 20 + 2s
So, t = 3s - 45 and t = 20 + 2s
3s - 45 = 20 + 2s
s = 65
So speed = s = 65 kmph
t = 20 + 2s
time = t = 20 + 2*65 = 150
Distance = st = 65 * 150 = 9750 km