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ICSE Class 8 Answered

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 | 19 Nov, 2015, 10:13: AM
answered-by-expert 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 | 19 Nov, 2015, 01:13: PM
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