Wiley Edge Time, Speed and Distance Quiz-3

Since the cars start at a 15-minute interval and meet the cyclist at a 12-minute interval, this means the cyclist is covering the distance between the cars in 3 minutes. The distance that the second car would have covered in the next 3 minutes was covered by the cyclist in his 12 minutes of movement after passing the first car.
(Speed of cyclist)*12=40*3;
speed of cyclist is 10mph.

Since E gives a start of 40 meters to D and D gives a start of 20 meters to C, the total start that E can give to C is the sum of the starts given by E to D and D to C, which is 40 meters + 20 meters = 60 meters.

Since Runner C already gives a head start of 25 meters to Runner B, to give a head start to Runner A, we need to add the head start distances. Therefore, 25 + 15 = 40 meters. Hence, Runner C can give a head start of 40 meters to Runner A.

Since X beats Y by 100 meters in a 2-kilometer race, it means X beats Y by 25 meters in every 500-meters. Similarly, Y beats Z by 80 meters in a 1-kilometer race, Y beats Z by 40 meters in every 500-meters. Therefore, in a 500-meter race, X and Z would be the combined difference of X's lead over Y and Y's lead over Z, which is 25+40=65 meters.

Since the train needed to cover the same distance in less time, it had to increase its speed. The increased speed is 50% higher than its usual speed.let the time taken to reach initially be t hrs so new time to reach will be (t-0.5)hrs. If we let the usual speed be x km/h, then the increased speed is 1.5x km/h. So the train travels the same distance with increased speed. Now equating the distance equations: ( t*x)=(t-0.5)*1.5x; t=1.5; substituting the value of t; we get x = 200 km/h. So increased speed = 1.5x = 300 km/h.

To find the average speed, we can use the formula: Average Speed = Total Distance / Total Time. Since the person covers one-third of the journey at 12 km/h and two-thirds at 6 km/h, we can calculate the average speed as follows:
Average Speed = (X+X+X)/{(X/12)+(X/6)+(X/6)}
Average Speed = 36/5
Average Speed = 7.2 km/h

Let the speed of the first car be x km/h. The speed of the second car is (x + 20) km/h.

The time taken by the first car to complete the journey is 500/x hours. The time taken by the second car to complete the journey is 500/(x + 20) hours. Since both cars reach city Y simultaneously, the time taken by both cars must be equal. Therefore, we can set up the equation 500/x = 500/(x + 20). Solving this equation, we find x = 40 km/h. The time spent by the slower car on the trip is 500/40 = 12.5 hours.

Since the boat's speed is 5:2 compared to the current, the time it takes to go along with the current is inversely proportional to the speed ratio.
Let the speed of the boat be 5x and the speed of the current be 2x. So, (speed downstream/speed upstream) = (5x+2x)/(5x-2x) = Time upstream/time downstream. Time upstream = (7/3)*(3.25) hours =7.6 hours.

Let's assume Ben's speed is S km/h. Since Alisha's speed is 6 km/h less than Ben's, her speed would be (S - 6) km/h. So they travel for the - exact same time before meeting.
(80-16)/(S-6) = (80+16)/S ; S=18 ; speed of alisha = (18 - 6) = 12 km/h.

Let's assume the speed of the boat in still water is x km/h. Since the boat is traveling upstream, its effective speed is reduced by the speed of the current, resulting in (x - 4) km/h.
Similarly, when the boat travels downstream, its effective speed is increased by the speed of the current, resulting in (x + 4) km/h.
We can set up the equation 10(x - 4) = 7.5(x + 4) to solve for x. Simplifying the equation, we find x = 28.