M. Tyra Solutions for Chapter: Time and Distance, Exercise 1: Exercises

A man walks from A to B and back in a certain time at the rate of $3\frac{1}{2} \mathrm{km}$ per hour. But if he had walked from A to B at the rate of $3 \mathrm{km}$ an hour and back from B to A at the rate of $4 \mathrm{km}$ an hour, he would have taken $5$ minutes longer. Find the distance between A and B.

A man rode out a certain distance by train at the rate of $25 \mathrm{km}$ per hour and walked back at the rate of $4 \mathrm{km}$ per hour. The whole journey took $5$ hours $48$ minutes. What distance did he ride?

Two trains start at the same time from two stations and proceed towards each other at the rates of $20 \mathrm{km}$ and $25 \mathrm{km}$ per hour respectively. When they meet, it is found that one train has travelled $80 \mathrm{km}$ more than the other. Find the distance between the two stations.

I have to be at a certain place at a certain time and I find that I shall be $15$ minutes too late, if I walk at $4 \mathrm{km}$ an hour; and $10$ minutes too soon, if I walk at $6 \mathrm{km}$ an hour. How far have I to walk?

A person going from Pondicherry to Ootacamond travels $120 \mathrm{km}$ by steamer, $450 \mathrm{km}$ by rail and $60 \mathrm{km}$ by horse transit. The journey occupies $13$ hours $30$ minutes, and the rate of the train is three times that of the horse transit and $1\frac{1}{2}$ times that of the steamer. Find the rate of the train.

Supposing that telegraph poles on a railroad are $50$ metres apart, how many will be passed by a car in $4$ hours if the speed of the train is $45 \mathrm{km}$ an hour?

Kim and Om are travelling from point A to B, which are $400 \mathrm{km}$ apart. Travelling at a certain speed, Kim takes one hour more than Om to reach point B. If Kim doubles her speed she will take $1$ hour $30$ mins less than Om to reach point B. At what speed was Kim driving from point A to B? (in $\mathrm{kmph}$ )

To reach point B from point A, at $4 \mathrm{pm}$, Sara will have to travel at an average spped of $18 \mathrm{kmph}$. She will reach point B at $3 \mathrm{pm}$ if she travels at an average speed of $24 \mathrm{kmph}$. At what average speed should Sara travel to reach point B at $2 \mathrm{pm}$ ?