CBSE Class 8 Answered

two trains with a speed of 35kms per hour and 28 per hour respectively. Starting at the same time, run in the opposite directions between two station A and B, 315km apart. Find when and where they will meet(from A)

Asked by ganeshbp18 | 08 Jul, 2014, 07:59: PM

Expert Answer

$G i v e n space t h a t space t h e space t w o space t r a i n s space s t a r t space a t space t h e space s a m e space t i m e. A l s o space g i v e n space t h a t space t h e space s p e e d space o f space t r a i n space A space i s space 35 space k m divided by h space a n d space t h e space s p e e d space o f space t r a i n space B space i s space 28 k m divided by h space a n d space t h e y a r e space m o v i n g space i n space t h e space o p p o s i t e space d i r e c t i o n s space f r o m space A space a n d space B. D i s tan c e space b e t w e e n space A space a n d space B space i s space g i v e n space a s space 315 space k m. L e t space t r a i n space A space m o v e s space a space d i s tan c e space o f space x space k m space a n d b y space t h a t space t i m e space t r a i n space B space m o v e s space a space d i s tan c e space o f space 315 minus x space a n d space t h e y space m e e t space a t space t h e space s a m e space t i m e. W e space k n o w space t h a t space T i m e space equals fraction numerator D i s tan c e over denominator S p e e d end fraction T h u s space t o space r u n space x space k m comma space t r a i n space A space t a k e s space equals space x over 35 space h o u r s A n d space f o r space B comma space t h e space t i m e space t a k e n space t o space r e a c h space 315 minus x space k m space equals fraction numerator 315 minus x over denominator 28 end fraction space h o u r s S i n c e space t h e y space m e e t space e a c h space o t h e r space a t space t h e space s a m e space t i m e comma space w e space h a v e comma space x over 35 equals fraction numerator 315 minus x over denominator 28 end fraction rightwards double arrow 28 x equals 35 open parentheses 315 minus x close parentheses rightwards double arrow 28 x equals 35 cross times 315 minus 35 x rightwards double arrow 28 x plus 35 x equals 11025 rightwards double arrow 63 x equals 11025 rightwards double arrow x equals 11025 over 63 rightwards double arrow x equals 175 space k m T i m e space t a k e n space b y space t o space t r a v e l space 175 space k m equals space x over 35 space h o u r s equals 175 over 35 equals 5 space h o u r s T h u s space t h e space t i m e space f o r space t h e space t w o space t r a i n s space t o space m e e t space i s space 5 space h o u r s. T h e y space m e e t space e a c h space o t h e r space w h e n space t h e space t r a i n space f r o m space s t a t i o n space A space t r a v e l l e d space a space d i s tan c e space o f space 175 space k m.$