Time, Speed and Distance

A person can walk a certain distance and ride back on the bike taking a total time of $37 \min$ and the person could walk both ways in $55 \min$. How long would it take me to ride both ways?

The ratio between the speeds of two trains is $7 : 8$, If the second train runs $400 \mathrm{km}$ in $4 \mathrm{hours}$, then find the speed of the first train.

Letters of the word $\mathrm{DIRECTOR}$ are arranged in such a way that all the vowels come together. Find total number of arrangements?

The average age of the Indian football team is $30 \mathrm{years}$. The average age of $5$ of the players is $29 \mathrm{years}$ and that of another set of $5$ players, totally different from the first five, is $27 \mathrm{years}$. If it is the captain who was not included in either of these two group, then find the age of the captain _____.

Sita sees her friends standing at a distance of $240 \mathrm{m}$ from his position. She increases her speed by $50\%$ and hence takes $20 \sec$ now to reach her.
(i) If she travels at the original speed, how much time will she take?
(ii) What was her original speed ?

A sum of money is to be distributed among A, B, C, D in the proportion of $5 : 2 : 4 : 3$. What is B's share, if C gets, $₹1000$ more than D ?

A person travels equal distance with the speed of $3 \mathrm{kmph}$, $4 \mathrm{kmph}$ and $5 \mathrm{kmph}$ and takes a total time of $47 \min$. Find the total distance.

A leak was found in a ship when it was$77 \mathrm{km}$ from the shore. It was found that the leak admits $2.25 \mathrm{tones}$ of water in $5.5 \min$. $92 \mathrm{tones}$of water will be sufficient to sink the ship. But the pumps can throw out $12 \mathrm{tones}$an $\mathrm{hour}$. Find the average rate of sailing at which the ship may reach the shore as it begins to sink.

From a point on a circular track $5 \mathrm{km}$ long, $\mathrm{A}, \mathrm{B}$ and $C$ started running in the same direction at the same time with speeds of $2\frac{1}{2} \mathrm{km} \mathrm{per} \mathrm{hour}$, $3 \mathrm{km} \mathrm{per} \mathrm{hour}$ and $2 \mathrm{km} \mathrm{per} \mathrm{hour}$ respectively. Then on the starting point all three will meet again after

Walking at the speed of $6 \mathrm{km}/\mathrm{hr}$, a person reaches his office $8 \min$ late. If he walks at the speed of 8 km/hr he reaches his office $3 \min$ early. What is the distance between house and office?

A train passes a man standing on the platform. If the train is $170 \mathrm{m}$ long and its speed is $72 \mathrm{kmph}$, how much time it took in doing so?

A man can cover a certain distance in $3 \mathrm{h} 36 \min$ if he walks at the rate of $5 \mathrm{kmph}$. If he covers the same distance on cycle at the rate of $24 \mathrm{kmph}$, then the time taken by him is ______

What should come in place of question mark in the following series:

$5, 15, 35, 75, 155, ?$

A race track has a circumference of $3000 \mathrm{m}$ the length of the race is $9000 \mathrm{m}$. The fastest and the slowest cart meet for the first time after the start of the race at the end of the length in $10 \min$. All the carts start at the same point and fastest cart moves at twice the speed of the slowest cart, what is the time taken by the fastest cart to finish the race ?

A motorist travels to a place $150 \mathrm{km}$ away at an average speed of $50 \mathrm{kmph}$ and returns at $30 \mathrm{kmph}$. His average speed for the whole journey in $\mathrm{kmph}$ is _____

A farmer travelled a distance of $61 \mathrm{km}$ in $9 \mathrm{hr}$. He travelled partly on foot with $4 \mathrm{km}/\mathrm{hr}$ and partly on bicycle with $9 \mathrm{km}/\mathrm{hr}$. The distance travelled on foot is:

An athlete runs $200 \mathrm{m}$ race in $24 \sec$. Find his speed.

A train covers a distance of $3584 \mathrm{km}$ in $2$ days $8$ hours. If it covers $1440 \mathrm{km}$ on the first day and $1608 \mathrm{km}$ on the second day, by how much does the average speed of the train for the remaining part of the journey differ from that for the entire journey?

The speed of a truck is $\frac{1}{3}$ the speed of a train. The train covers $1230 \mathrm{km}$ in $5 \mathrm{h}$. What is the speed of truck?

A ship is moving at a speed of $30 \mathrm{kmph}$. To know the depth of the ocean beneath it sends a radio wave which travels at a speed $200 \frac{\mathrm{m}}{\sec }$. The ship receives the signal after it has moved $500 \mathrm{m}$. Find the depth of the ocean.