races Questions

In a 200-m race, if A gives B a head start of 35m, then A wins the race by 20sec. Alternatively, if A gives B a head start of 55m, the race ends in a dead heat. How long does A take to run 200m?

In a 3000m race, if vehicle A gives vehicle B a start of 400m, then vehicle A wins the race by 10s. If vehicle A gives vehicle B a start of 750m, then the race ends in a dead heat. How long does vehicle A take to run 3000m?

In a 150m race, if R gets a 5m head start, then he would beat S by 35m. If S gets a 25m head start in a 100m race, then ________ would win the race by ___________ metres.

A beats B by 125 m in a kilometre race. Find B’s speed if A’s speed is 16 m/sec.

Jaya and Hima are competing in a $200\text{meter}$ race. Both start the race at the same time, but Jaya starts the race $40\text{meters}$ ahead of the starting point, whereas Hima starts the race at the starting point. Assume that Hima runs at a speed of $10\text{meters per second}$, whereas Jaya runs at a speed of $x\text{meters per second}$. If both reach the finish line at the same time, then what is the value of $x$?