1. a farmer travelled a distance of 61 km in 9 hr . he travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr . find the distance travelled by him on foot.
 
2. rohan cycles to his offic at the rate of 25/2 km/hr and is late by 3 minutes. however , if he travels at 15 km/hr , he reaches 5 minutes earlier than the usual time . what is the distance of his office from his residence ? 
 
3. robert is travelling in his cycle and has calculated to reach point A at 2 pm . if he travels at 10 km/hr . however he will reach there at 12 noon if he travels at 15 km/hr . at what speed must he travel to reach A at 1 pm ? 

Asked by Rishi | 19th Nov, 2015, 10:13: AM

Expert Answer:

begin mathsize 16px style Total space distance space covered space by space the space farmer space equals space 61 space km Total space time space taken space equals space 9 space hrs. Distance space travelled space on space foot space at space speed space of space 4 space km divided by hr Let space straight d subscript 1 space be space the space distance space travelled space on space foot space and space straight t subscript 1 space be space the space time space taken space while space travelling space on space foot therefore straight d subscript 1 space equals space 4 space cross times space straight t subscript 1 equals 4 straight t subscript 1 space... left parenthesis 1 right parenthesis Distance space travelled space on space bicycle space at space speed space of space 9 space km divided by hr Let space straight d subscript 2 space be space the space distance space travelled space on space foot space and space straight t subscript 2 space be space the space time space taken space while space travelling space on space foot therefore straight d subscript 2 space equals space 9 space cross times space straight t subscript 2 equals 9 straight t subscript 2 space space... left parenthesis 2 right parenthesis Total space distance space equals straight d subscript 1 plus straight d subscript 2 space equals space 61 space km space space... left parenthesis 3 right parenthesis Total space time space taken space equals space straight t subscript 1 plus space straight t subscript 2 space equals space 9 space hrs space... left parenthesis 4 right parenthesis From space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis comma space left parenthesis 3 right parenthesis space and space left parenthesis 4 right parenthesis straight d subscript 1 plus straight d subscript 2 equals 4 straight t subscript 1 plus space 9 straight t subscript 2 space therefore 4 straight t subscript 1 plus space 9 straight t subscript 2 equals space 61 space space... left parenthesis straight a right parenthesis From space left parenthesis 4 right parenthesis comma space space straight t subscript 1 plus space straight t subscript 2 space equals space 9 therefore 4 straight t subscript 1 plus 4 straight t subscript 2 space equals space 36 space space... space left parenthesis straight b right parenthesis left parenthesis multiplying space each space term space by space 4 right parenthesis Subtracting space left parenthesis straight b right parenthesis space from space left parenthesis straight a right parenthesis space 4 straight t subscript 1 plus space 9 straight t subscript 2 minus open parentheses 4 straight t subscript 1 plus 4 straight t subscript 2 close parentheses equals space 61 minus space 36 therefore space 4 straight t subscript 1 space minus 4 straight t subscript 1 plus space 9 straight t subscript 2 minus 4 straight t subscript 2 equals space 25 therefore 5 straight t subscript 2 space equals space 25 space rightwards double arrow straight t subscript 2 space equals space 5. therefore Time space taken space on space bicycle space equals space 5 space hrs. straight t subscript 1 plus space straight t subscript 2 space equals space 9 space rightwards double arrow space straight t subscript 1 space equals space 9 minus 5 space equals space 4 space hr Hence comma space time space taken space by space travelling space on space foot space equals space 4 space hrs. straight d subscript 1 space equals space 4 space cross times space straight t subscript 1 equals 4 space cross times space 4 space equals space 16 space therefore Distance space travelled space on space foot space equals space space 16 space km  end style
 
 
 
 
 
 
 
 
 
 
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Answered by Priti Shah | 19th Nov, 2015, 01:13: PM