Question : Motorcyclist P started his journey at a speed of 30 km/h. After 30 minutes, motorcyclist Q started from the same place but with a speed of 40 km/h. How much time (in hours) will Q take to overtake P?
Option 1: $1$
Option 2: $\frac{3}{2}$
Option 3: $\frac{3}{8}$
Option 4: $2$
Correct Answer: $\frac{3}{2}$
Solution : Relative speed in the same direction = (40 – 30) = 10 km/hr Distance covered by P in 30 minutes, = $(30×\frac{1}{2})=15$ km The time it will take Q to overtake P = $\frac{15}{10}$ = $\frac{3}{2}$ hr Hence, the correct answer is $\frac{3}{2}$.
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Question : A car completed a journey of 400 km in $12\frac{1}{2}$ hours. The first $\frac{3}{4}$th of the journey was done at 30 km/hr. Calculate the speed for the rest of the journey.
Option 1: 45 km/hr
Option 2: 25 km/hr
Option 3: 40 km/hr
Option 4: 30 km/hr
Question : A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance?
Option 1: 7 hours 15 minutes
Option 2: 5 hours 45 minutes
Option 3: 6 hours
Option 4: 5 hours 15 minutes
Question : A motorcyclist left $6\frac{6}{9}$ minutes later than the scheduled time but to reach its destination 21 km away on time, he had to increase his speed by 12 km/hr from the usual speed. What is the usual speed (in km/h) of the motorcyclist?
Option 1: 28
Option 2: 35
Option 3: 42
Option 4: 64
Question : A man goes from place A to B at a speed of 12 km/hr and returns from B to A at a speed of 18 km/hr. His average speed for the entire journey is:
Option 1: $14 \frac{2}{5} \mathrm{~km} / \mathrm{hr}$
Option 2: 15 km/hr
Option 3: 6 km/hr
Question : A boat can travel 104 km downstream in 8 hours. If the speed of the stream is 2 km/hr, then at what time will it be able to cover 13 km upstream?
Option 1: $2 \frac{2}{3}$ hours
Option 2: $1 \frac{4}{9}$ hours
Option 3: $2 \frac{1}{2}$ hours
Option 4: $1 \frac{2}{3}$ hours
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