Question

rajan travelled 320 km by train and 180 km by car, taking 7 hours. but, if he travels 160 km by train and 240km by car. he takes 1 hour less. find the speed of the train and that of the car. use simultaneous equation

Answer 1

let , the speed of train be x

the speed of car be Y

we know that time =distance /speed

According to problem ,

he travelled 320 km by train and 180 km by car , taking 7 hours

therefore , 320/x + 180 /Y = 7 --------(1)

he travels 160 km by train and 240km by car ,. he takes 1 hour less

therefore , 160/x +240/Y = 6 --------(2)

we taken 1/x =p , 1/Y =q

then eq (1) =320p+ 180q=7. ---------(3)
and eq (2)= 160p+240q=6 --------(4)

using elimination method

equation (3) × 1. 320p+180q=7

equation (4) × 2. 320p+ 480q= 12
(-). (-). (-)
-----------------------------
- 300q = - 5

therefore. q = 5/300 = 1/60

submit q=1/60 in equation (3)

= 320p +180( 1/60) =7

= 320p = 7-3 =4

=. p = 4/ 320

therefore p= 1/ 80

we know that 1/x=p. 1/Y =q

then x = 80 ; Y = 60

therefore , the speed of the train = 80 kmph

the speed of car =. 60 kmph

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