Ram and Shyam start at the same time towards each other by cycle from two places 90 km apart. If the speeds be 8km/hr and 7km/hr respectively, find the distance between them after 4 hours. Find also the difference after 8 hours.

Ram and Shyam start at the same time towards each other by cycle from

1.	Ram and Shyam start at the same time towards each other by cycle from two places 90 km apart. If the speeds be 8km/hr and 7km/hr respectively, find the distance between them after 4 hours. Find also the difference after 8 hours.
Answer» Let X and Y be two cars starting from points A and B RESPECTIVELY. Let the speed of CAR X be x km/hr and that of car Y be y km/hr.Case I When two cars move in the same directions:Suppose two cars meet at point Q. Then,DISTANCE travelled by car X=AQ,Distance travelled by car Y=BQIt is GIVEN that two cars meet in 9 hours.∴ Distance travelled by car X in 9 hours =9x km.⇒AQ=9xDistance travelled by car y in 9 hours =9y km.⇒BQ=9yClearly, AQ−BQ=AB⇒9x−9y=90 [∵AB=90km]⇒x−y=10 (i)Case II When two cars move in opposite directions:Suppose two cars meet at point P. Then,Distance travelled by car X = AP,Distance travelled by car Y = BPIn this case, two cars meet in 79 hours.∴ Distance travelled by car X in 79 hours = 79 xkm⇒BP= 79 yClearly, AP+BP=AB⇒ 79 x+ 79 y=90⇒ 79 (x+y)=90⇒x+y=70 .(ii)Adding equations (i) and (ii), we get2x+0=80⇒x=40Putting in (ii), we get, y=70−40=30∴x=40 and y=30.Hence, the speed of car X is 40 km/hr and speed of car Y is 30 km/hr.