Question
Tue April 21, 2015 By: Jeel Katira

a car travels a certain distance with  a certain speed.
if it had traveled 263646473.556596 km/hour faster it would have reached the destination 6364.356357 hours earlier but if it had traveled 446436.6466834 km/hour slower then it would be 645464.564563 hours late. What is its original speed and distance and time taken?

Expert Reply
satyajit samal
Wed April 22, 2015
L e t space a equals 263646473.556596 space k m divided by h r b equals 446436.6466834 space k m divided by h r c equals 6364.356357 space h r d equals 645464.564563 space h r L e t space t h e space o r i g i n a l space s p e e d space b e space V space a n d space o r i g i n a l space t i m e space t a k e n space b e space T. space T h e space t o t a l space d i s tan c e space t r a v e l l e d space b e space S. i f space i t space h a d space t r a v e l e d space a equals 263646473.556596 space k m divided by h o u r space f a s t e r space i t space w o u l d space h a v e space r e a c h e d space t h e space d e s t i n a t i o n space c equals 6364.356357 space h o u r s space e a r l i e r S o space a s space p e r space t h e space q u e s t i o n comma S equals left parenthesis V plus a right parenthesis left parenthesis T minus c right parenthesis.... left parenthesis 1 right parenthesis S i m i l a r l y comma space i f space i t space h a d space t r a v e l e d space b equals 446436.6466834 space k m divided by h o u r space s l o w e r space t h e n space i t space w o u l d space b e space d equals 645464.564563 space h o u r s space l a t e. space S o comma S equals left parenthesis V minus b right parenthesis left parenthesis T plus d right parenthesis.... left parenthesis 2 right parenthesis S equals V T.... left parenthesis 3 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 3 right parenthesis space w e space g e t space left parenthesis V plus a right parenthesis left parenthesis T minus c right parenthesis equals V T.... left parenthesis 4 right parenthesis F r o m space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis space w e space g e t space left parenthesis V minus b right parenthesis left parenthesis T plus d right parenthesis equals V T.... left parenthesis 5 right parenthesis S i m p l i f y i n g space left parenthesis 4 right parenthesis space w e space g e t space minus V C plus a T minus a c equals 0... left parenthesis 6 right parenthesis S i m p l i f y i n g space left parenthesis 5 right parenthesis space w e space g e t V d minus b T minus b d equals 0... left parenthesis 7 right parenthesis E l i m i n a t i n g space apostrophe T apostrophe space f r o m space left parenthesis 6 right parenthesis space a n d space left parenthesis 7 right parenthesis space w e space g e t V equals fraction numerator a b left parenthesis c plus d right parenthesis over denominator a d minus b c end fraction S i m i l a r l y space e l i m i n a t i n g space apostrophe V apostrophe space f r o m space left parenthesis 6 right parenthesis space a n d space left parenthesis 7 right parenthesis space w e space g e t T equals fraction numerator c d left parenthesis a plus b right parenthesis over denominator a d minus b c end fraction N o w space u sin g space t h e space v a l u e s space o f space a comma space b comma space c space a n d space d comma space w e space g e t space T equals 6364.46262 space h r V equals 450 comma 846.0918 space k m divided by h r S equals V T almost equal to 2 comma 869 comma 393 comma 099 space k m
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