Arun Sharma Solutions for Exercise 4: Exercise on Application of Time, Speed and Distance

How many times between $2$ PM and $4$ PM does the minutes and coincide with the seconds hand?

A man enters his house at some time between$6 to 7$PM. When he leaves his house some time between $7 to 8$, he observes that the minute hand and the hour hand have interchanged positions. At what exact time did the man enter the house?

Two friends started simultaneously from Kanpur towards Lucknow in the same direction along a straight road. The faster friend Raveesh was on a bike while Prakash was in an auto. The ratio of their speeds was $1:5$ respectively. Two hours later, Raveesh parked his bike and started running back towards Prakash's auto. His speed dropped by $80\%$ as a result of this. They meet at a point which is $15$km from Kanpur. What was the speed of the auto?

Two brothers came to know about their sister's wedding at the last minute. The wedding was to be held at a location which was $800$ kms away from Mumbai where both of them lived. The elder brother Kanhaiya came to know about the wedding at $6$ PM and left immediately in his car. His younger brother Ramaiyya came to know about the wedding at $9:30$ PM and left in his car immediately at a speed which was $15$ kmph higher than the speed of his elder brother, At $4:30$ AM it was found that the two cars were had travelled continuously  without taking any rest, find the speed(in km/hr) of Kanhaiya's car.

Ranatunga once challenged Bolt to a race. The distance of the race was set at $2 \mathrm{km}$. They start at the same time and the ratio of their speeds is seen to be $4: 1$ (obviously Bolt would be faster). After some time passes, Bolt realises that he is far ahead and calculates that even if he stops for a snack and a nap for ' $\mathrm{n}$ ' minutes, he would still reach his destination and beat Ranatunga by $13$minutes. Hence, he plans to take a break of 'n' minutes. Ranatunga keeps walking during this whole time. However, when Bolt wakes up, he realises that he has stopped for a total of $(\mathrm{n}+15)$ minutes. He redoubles his efforts by increasing his speed to double his original speed. The race eventually ended in a dead heat. If it is known that Bolt overstayed his stop by $\frac{6\mathrm{n}}{5}$ mins, how long did Ranatunga take to complete the race?

$\mathrm{A}$ and $\mathrm{B}$ run a $300 \mathrm{m}$ race where the initial speed of $\mathrm{B}$is double the speed of A. After some time, going on these speeds, A realising that he would be losing the race redoubled his effort and increased his speed to four times his initial speed. As a result, they reached the end point at the same time and the race resulted in a dead heat. What was the distance travelled by B, when A quadrupled his speed?

Amit and Bimal start running around a circular track of circumference $4200$metres. Their respective speeds are $15 \mathrm{m}/\mathrm{s}$ and $3 \mathrm{m}/\mathrm{s}$. Their ${14}^{\mathrm{th}}$meeting occurs at point $\mathrm{P}$ and their ${22}^{\mathrm{nd}}$meeting occurs at the point Q. Find the longer distance (along the circumference) between Points P and Q.

In a $2 \mathrm{km}$ race, Ravi beats Sandeep by $45$seconds and Sandeep beats Tarun by a further $75$seconds. In the same race, Ravi beats Tarun by $400 \mathrm{m}$. Find the time in which Ravi can run the race (in seconds).