HAT MCQs

The required numbers multiply to 6 and add to 5.
Those numbers are 2 and 3.

To convert km/h to m/s, multiply by 5/18.
Thus, 54 × 5/18 = 15 m/s.

Let total distance be 3d; time is d/30 + 2d/60 = d/15.
Average speed is 3d ÷ (d/15) = 45 km/h.

To convert m/s to km/h, multiply by 18/5.
Thus, 20 × 18/5 = 72 km/h.

Travel time is 210 ÷ 70 = 3 hours.
Three hours after 8:00 a.m. is 11:00 a.m.

Time equals distance divided by speed.
Thus, 12 ÷ 4 = 3 hours.

Their closing speed is 20 + 25 = 45 km/h.
Time = 90 ÷ 45 = 2 hours.

For equal distances, average speed is the harmonic mean 2ab/(a + b).
Thus, 2 × 40 × 60 ÷ 100 = 48 km/h.

The path forms a right triangle with legs 5 and 12.
By Pythagoras, distance is √(25 + 144) = 13 km.

For equal time intervals, average speed is the arithmetic mean.
Thus, (40 + 60)/2 = 50 km/h.

The first part takes 2 hours and the second takes 1 hour.
The total travel time is 3 hours.

For opposite directions, relative speeds are added.
Thus, 50 + 70 = 120 km/h.