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ICSE Class 10 Answered

A motorist leaves his home at 8 a.m. to go to a place 90 km away. If he drives at an average speed of (x-5) km/hr, he will be15 minutes late for his appointment. If he drives at a speed of (x+10) km/hr, he will be 15 minutes early. Find the value of x and the time fixed for his appointment.
Asked by khushdab | 02 Apr, 2020, 04:27: PM
answered-by-expert Expert Answer
The average speed is x km/hr
Let the time taken be t.
If he drives at an average spee of (x-5) km/hr, he will be 15 minutes late and if he drives at an average spee of (x+10) km/hr, he will be 15 minutes early.
According to these conditions, we have
t plus 15 over 60 equals fraction numerator 90 over denominator x minus 5 end fraction space space i. e. space space t plus 1 fourth equals fraction numerator 90 over denominator x minus 5 end fraction space... space left parenthesis i right parenthesis t minus 15 over 60 equals fraction numerator 90 over denominator x plus 10 end fraction space space i. e. space space t minus 1 fourth equals fraction numerator 90 over denominator x plus 10 end fraction space... space left parenthesis i i right parenthesis S u b t r a c t i n g space left parenthesis i i right parenthesis space f r o m space left parenthesis i right parenthesis comma space w e space g e t 1 half equals fraction numerator 90 over denominator x minus 5 end fraction minus fraction numerator 90 over denominator x plus 10 end fraction rightwards double arrow left parenthesis x minus 5 right parenthesis left parenthesis x plus 10 right parenthesis equals 180 left parenthesis x plus 10 minus x plus 5 right parenthesis rightwards double arrow x squared plus 5 x minus 50 equals 180 cross times 15 rightwards double arrow x squared plus 5 x minus 2750 equals 0 rightwards double arrow x equals fraction numerator negative 5 plus-or-minus square root of 25 plus 11000 end root over denominator 2 end fraction equals fraction numerator negative 5 plus-or-minus square root of 11025 over denominator 2 end fraction equals fraction numerator negative 5 plus-or-minus 105 over denominator 2 end fraction rightwards double arrow x equals negative 55 space o r space 50 S i n c e comma space t h e space s p e e d space c a n apostrophe t space b e space n e g a t i v e. H e n c e space t h e space v a l u e space o f space x space i s space 50. T i m e equals 90 over 50 equals 1.4 equals 1 space h o u r space 24 space m i n u t e s.
Answered by Renu Varma | 03 Apr, 2020, 11:48: AM

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