TIME, SPEED & DISTANCE (LEVEL - 2)
Q1–10 of 50A boy is running at a speed of p kmph to cover a distance of 1 km. But, due to the slippery ground, his speed is reduced by q kmph (p > q). If he takes r hours to cover the distance, then
Effective speed = \(p-q\) kmph.
\[ \text{Time } r = \frac{\text{Distance}}{\text{Speed}} = \frac{1}{p-q} \]
\[ \frac{1}{r}=p-q \]
Answer: (a) \(\frac{1}{r}=p-q\)
Ravi can walk a certain distance in 40 days when he rests 9 hours a day. How long will he take to walk twice the distance, twice as fast and rest twice as long each day?
Initial working hours per day = \(24 - 9 = 15\) hours/day.
Rest time is doubled: \(2 \times 9 = 18\) hours/day.
Therefore, new working hours per day: \(24 - 18 = 6\) hours/day.
Using the chain rule formula:
$$ \frac{W_1}{S_1 \times T_1 \times D_1} = \frac{W_2}{S_2 \times T_2 \times D_2} $$ $$ \frac{D}{1 \times 15 \times 40} = \frac{2D}{2 \times 6 \times D_2} $$ $$ \frac{D}{600} = \frac{D}{6D_2} $$ $$ 600 = 6D_2 $$ $$ D_2 = 100\text{ days} $$A car is driven at the speed of 100 km/hr and stops for 10 minutes at the end of every 150 km. To cover a distance of 1000 km, it will take
Stops occur at $150, 300, 450, 600, 750, 900\text{ km}$ (total $6\text{ stops}$).
Answer: (c) 11 hours
A man takes 50 minutes to cover a certain distance at a speed of 6 km/hr. If he walks with a speed of 10 km/hr, he covers the same distance in
Answer: (c) 30 minutes
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is
Since ratio is $7 : 8$:
Answer: (d) 87.5 km/hr
A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
\(21\text{ posts}\) form \(20\text{ gaps}\) of \(50\text{ m}\).
$$ \text{Distance} = 20 \times 50 = 1000\text{ m} = 1\text{ km} $$ $$ \text{Speed} = \frac{1\text{ km}}{1\text{ minute}} = \frac{1\text{ km}}{\frac{1}{60}\text{ hr}} = 60\text{ km/hr} $$Answer: (c) \(60\text{ km/hr}\)
An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?
Stops occur at $75, 150, 225, 300, 375, 450, 525\text{ km}$ ($7\text{ stops}$).
Answer: (a) 6 hrs 21 min
A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is :
Let cyclist distance \(= D\) and time \(= T\).
$$ \text{Speed}_c = \frac{D}{T} $$Jogger distance \(= \frac{D}{2}\) and time \(= 2T\).
$$ \text{Speed}_j = \frac{D/2}{2T} = \frac{D}{4T} $$ $$ \text{Ratio} = \frac{\text{Speed}_j}{\text{Speed}_c} = \frac{1/4}{1} = 1:4 $$Answer: (c) \(1:4\)
A motor car starts with the speed of 70 km/hr with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?
First $2\text{ hours}$ at $70\text{ km/hr} = 140\text{ km}$.
Next $2\text{ hours}$ at $80\text{ km/hr} = 160\text{ km}$.
Distance covered in $4\text{ hours} = 300\text{ km}$.
Remaining distance $= 345 - 300 = 45\text{ km}$.
Speed in 5th hour $= 90\text{ km/hr}$.
Time needed $= \frac{45}{90} = 0.5\text{ hrs} = 30\text{ mins}$.
Answer: (c) 4 hrs 30 minutes
A bus moving at a speed of 24 m/s begins to slow at a rate of 3 m/s each second. How far does it go before stopping?
Using $v^2 = u^2 - 2as$, where $v=0, u=24, a=3$:
Answer: (d) 96 m