Time, Speed and Distance

Peter and Paul start simultaneously on 2 different cars from Point A and travel towards Point B at speeds of 52 kmph and 39 kmph respectively on the same road. As soon as Peter reaches Point B, he returns back to Point A on the same road and meets Paul on the way. How far from Point B do the two friends meet, if the distance between the 2 points is 70 kms?

Directions: Answer the questions independently of each other. Two people start their journies from point A to B with an initial speed of 10 km/hr. The first person then increases his speed by 10 km/hr for every successive 10% of the distance till B, whereas the second person increases his speed by 10 km/hr for every successive 10% of the time of his journey till he reaches B. Who reaches B first?

Anup's car broke down after he had covered 1 4 t h of the distance from his home to his office. He then boarded a bus, which took him to his office. He realised that to reach his office on that day, it took him 9 times as long travelling by bus as travelling by his car. How many times the speed of the bus is the speed of the car?

Raghu sets off on his bike from Asansol towards Kolkata at a certain speed, intending to reach Kolkata at 10 AM. After covering a certain distance, he realises that he would be able to cover only three-fourth of the intended distance by 10 AM. He, therefore, increases his speed by 50% and reaches Kolkata at 10 AM. What fraction of the total distance did he cover at his initial speed?

In an open field, two cyclists start from different points and ride towards a common point. They meet at that point. After meeting, one cyclist rides south while the other rides west. Two hours later, they are 17 km apart. If the speed of one cyclist is 0.5 km/h less than twice the speed of the other cyclist, find the distance between them four hours before they met.

Two athletes, Alex and Bob, start running simultaneously from a certain point on a circular track of length 800 m in opposite directions with speeds in the ratio 5 : 3. Which of the following gives a possible value of the distance (in m) of the starting point from the point on the track where their fourth meeting takes place?

Last Saturday Keshav visited his friend who lived in a village on his motorbike. Part of the distance was on mud road which he covered at 16 km/h, whereas the remaining was on gravel which he covered at a speed which was 9 km/h more than that on mud road. If he covered a total distance of 90 km in four and a half hours, for how long (in hours) did he travel on gravel?

Dagestan is a province in the Russian Republic known for its hilly terrains. Kadirov, a cab driver, was travelling from city P to city Q (in Dagestan). The distance between the two cities P and Q is partly uphill, party downhill and party on level ground. It took Kadirov 140 minutes to travel from P to Q covering a total distance of 72 km. How much time (in minutes) did he take on his return journey from Q to P if the uphill speed, the downhill speed and the speed of the cab on level ground are 30 km/hr, 45 km/hr and 36 km/hr, respectively?

Two cars 𝐶₁ and 𝐶₂ start simultaneously from two cities 𝑃 and 𝑄, moving towards each other. They meet for the first time 30 km away from 𝑄. After meeting they exchange their speeds as well as the direction in which they were moving and proceed to travel towards their respective starting points. Upon reaching their starting points, they turn back with the same speed and meet for the second time at a point which is 10 km away from 𝑃. Which of the following gives the distance between 𝑃 and 𝑄 (In km)

On a straight line AB of length 120 m, there is a point C which is 40 m away from A and 80 m away from B. P and Q started cycling from C at respective speeds of 5 m/s and 3 m/s, with P moving towards A and Q moving towards B. As soon as they reach A and B, respectively, they start cycling towards B and A and continue moving in a to-and-fro motion. At what distance (in m) from A will they meet each other for the second time?

Two boats A and B started rowing downstream from P simultaneously at different constant speeds and another boat C started rowing upstream from Q at the same time. If A crossed C at a point, which is at a distance of three-fourth of PQ from P and then B crossed C at a distance of two-third of PQ from P, and the upstream speed of boat C is 1 km/h, then which of the following gives the difference between the upstream speeds, in km/h, of boats A and C?