Question

i
Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours
if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels
200 km by train and rest by car. Find the speed of the train and the car.

Answer 1

speed=distance/time

let speed of train= x km/h

let speed of car= y km /h

total distance travelled a part= 600km

distance by train=120km

distance by car=600-120=480km

total time =8hours

so, according to the question

(120/x)+(480/y)=8 ((1))

in second case similarly

(200/x)+ (400/y)= 8+(20/60) ==8+(1/3)==25/3 ((2))

to reduce equation ((1)) and ((2)) into linear equation

let( (1/x)=a )) ( (1/y=b) )

so equation change

120a+480b= 8. ((3))

200a+400b=25/3((4))

multiply ((3)) by 5 and ((4)) by 3

600a +2400b =40. ((5))

600a+1200b=(25/3)*3==25. ((6))

subtracting ((6)) from ((5))

600a+2400b=40

600a+1200b=25

(-). (-). =(-)

1200b=15

b= 15 /1200

b=1/80

as b=1/y =1/80 so

y=80

put value of b in ((5))

600a+(2400*1/80)=40

600a + 30=40

600a=40-30=10

a=10/600

a=1/60=1/x

inversely x=60

Hence

(speed of train)x = 60km/h

(speed of car )y =80 km/h

it's over

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