Time and Distance
Two cars (A and B) start at the starting line at the same time on a 3-mile long circular track, going in opposite directions. As they drive around the course, they pass each other many times. Exactly one hour after starting, they pass each other for the 33rd time. At this point car A has completed exactly 20 laps. What is the average speed of Car B?
One of the ski lifts at Kulu Manali climbs the mountain in a line that parallels one of the ski runs. Both the run and the lift are two km long, and a chair passes the starting point of the lift every 10 seconds. A skier starts her run just as the chair arrives at the top of the lift and another chair starts back down. She arrives at the bottom just as a chair is starting up the mountain and another chair is completing its descent. Counting these two chairs and the two at the start of her run, she sees 97 chairs on their way up the mountain and 61 chairs on their Way down. If the chair that started down the slope at the same time that the skier did is still on its way down when the skier reaches the bottom of the slope, what is the average speed of the skier?
At what time instant after 8 o' clock do the short hand and long hands of a clock enclose the equal angles with the horizontal?
Akbar & Birbal start together on a circular track of 600 m in opposite directions at 6m/s and 4m/s respectively. Every time they meet, they exchange their speeds as well as directions. Find out the shortest distance of their 7th meeting point from the starting point along the track.
Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/h. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2, respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and shyam’s return
to the point A is (2003)