Rail engine is moving at uniform speed of 30 kilometre per hour towards the place X when the engine is still 20 kilometres away from X an insect start at x and shuttles between X and engine at a uniform speed of 42 km per hour the total distance travelled by the insect bite the time engine reaches X
Answers
hey mate here is your answer
answer is 28km
.
Relative speed = 30+42=72km/hr
therefore, the rail engine and insect will meet for the first time after
=20/72
therefore, distance covered by the insect in this interval
20/72 * 42
=35/3km
in this time the engine covered a distance =20/72 * 30=25/3km
As the insect will return to X in that time engine will again cover a distance
=25/3km
so, the distance left= 20-25/3+25/3=10/3
Again the rail engine and the insect will meets for the second time after
10/3*72
=5/108 hours
therefore, distance covered in this time by the insect
=5*42/108
=35/18 km
In returning it will describe a distance
35/18
therefore, distance coverd by insect
= 70/3+70/18+........
=70/3(1+1/6+....)
= 70/3 * 1/1-1/6
70/3*1/5/6 = = 70/3*6/5
= 28km
hope it helps you
pls
pls mark me as a brainlist
plz don't use the above answer as it is very long as this question is from tallentex( a scholarship exam), and in this type of exam, there should be a shorter solution
here is the shorter solution
since 20km distance was left and the train was uniformly moving with 30km per hour, then the time it will take to cover this leftover distance will be:-
30kilometer=1hour
so,20km= (1/30) * 20 = 20/30 = 2/3 hour (we will not simplify it as then it will be tough to calculate later