Dinesh is travelling on his bike. He will reach point P at 6 p. m. if he travels at 20 km/h. He will reach point P at 2 p. m. if he travels at 30 km/h. At what speed must he travel to reach point P at 4 p. m.?

Let the total distance to point P be D km, and let the time taken to reach at 4 p.m. be T hours.
The time difference between reaching at 2 p.m. and 6 p.m. is 6−2=4 hours.

Using the formula Time=
Speed
Distance
​
:

20
D
​
−
30
D
​
=4
Finding a common denominator (60):

60
3D−2D
​
=4
60
D
​
=4⟹D=240 km
Now, calculate the time taken at 30 km/h:

Time taken=
30
240
​
=8 hours
Since he reaches at 2 p.m. after travelling for 8 hours, he must have started at:

2 p.m.−8 hours=6 a.m.
To reach point P at 4 p.m., the total travel duration from 6 a.m. is:

4 p.m.−6 a.m.=10 hours
Required speed to cover 240 km in 10 hours:

Speed=
10
240
​
=24 km/h