Time, Speed and Distance

A thief seeing a policeman from a distance of $200$ metres starts running at a speed of $8$ km/hr. The policeman gives chase immediately with a speed of $9$ km/hr and the thief is caught. What is the distance run by the thief?

A boat covers a certain distance downstream in 1 hour, while it comes back in $1\frac{1}{2}$ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

$A$ and $B$ are standing at place $P$. They start moving in the opposite directions at the speed of $5\ kmph$ and $4\ kmph$ respectively. What will be the distance between them after $3$ hours?

A man can reach a certain place in $30$ hours. If he reduces his speed by $\displaystyle \dfrac {1}{15}$th, he goes $10$ km less in that time. Find his speed in km/ hr?

A truck covers a distance of $550$ metres in $1$ minute whereas a bus covers a distance of $33$ km in $45$ minutes. What is the ratio of their speeds?

$P$ and $Q$ are two railways stations which are $560$ km apart. An express train leaves stations $P$ to stations $Q$ at a speed of $55$ km/hr and a passenger train leaves station $Q$ to station $P$ at a speed of $25$ km/hr, both at the same time. Find when and where will the both trains meet.

A person drives his car for $3$ hours at a speed of $40$ km/hr and for $4.5$ hours at a speed of $60$ km/hr. At the end of it, he finds that he was covered $\displaystyle \frac {3}{5}$ of the total distance. What is the uniform speed with which he should further drive to cover the remaining distance in $4$ hours?

A and B walk round a circular track They start at 8 am from the same point in opposite directions A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively How many times shall they cross each other before 9.30 am

A car travelling with $\displaystyle \dfrac{5}{7} $ of its usual speed covers $42$ km in $1$ hour $40$ min $48$ sec. What is the usual speed of the car?

A thief is spotted by a policeman from a distance of $100$ metres. When the policeman starts the chase the thief also starts running. If the speed of the thief is $8$ km/hr and that of the policeman $10$ km/hr, how far the thief will have to run before he is overtaken ?

Robert is travelling on his cycle and has calculated to reach point $A$ at $2$ $p.m.$ If he travels at $10$ $kmph$, he will reach there at $12$ noon, if he travels at $15$ $kmph$, at what speed must he travel to reach $A$ at $1$ $p.m.$

With a uniform speed a car covers the distance in $8$ hours. Had the speed been increased by $4$ km/hr the same distance could have been covered in $\displaystyle 7\frac{1}{2}$ hours. What is the distance covered ?