Question 1
A man has to cover 80 km in 3 hours. He covers 20 km in the first hour and then halts for 20 minutes. By what factor must he increase his speed, relative to his first-hour speed, to arrive on schedule?
Show solution
Remaining distance = 80 − 20 = 60 km Remaining time = 3 hr − 1 hr (travelled) − 20 min (halt) = 5/3 hr Required speed = 60 ÷ 5/3 = 36 km/hr First-hour speed = 20 km/hr Factor = 36/20 = 1.8
Question 2
A delivery van must cover 45 km in 2½ hours. It covers 15 km in the first hour, then waits 30 minutes at a checkpoint. By what factor must it increase its speed?
Show solution
Remaining = 30 km. Remaining time = 2.5 − 1 − 0.5 = 1 hr Required speed = 30 km/hr; first-hour speed = 15 km/hr Factor = 2
Question 3
A car covers a certain distance in 40 minutes. If its speed is reduced by 12 km/hr, it takes 50 minutes. Find the original speed and the distance.
Show solution
Let original speed = S. Distance is the same both times. S × (2/3) = (S − 12) × (5/6) Multiply by 6: 4S = 5S − 60 → S = 60 km/hr Distance = 60 × 2/3 = 40 km