manoj travels 600 km to his home partly by train and partly by car .he takes 8 hrs if he travels 120 km by train and rest by car. he takes 20 min longer if he travels 200 km by train and rest by car. Find the speed of the train and the car
Answers
Step-by-step explanation:
TOTAL DISTANCE : 600 km
LET THE SPEED OF TRAIN BE X km/h
LET THE SPEED OF CAR BE Y km/h
GIVEN THAT ,He takes 8 hrs if he travels 120 km by train and rest by car.
∴TIME TAKEN TO TRAVEL BY TRAIN : (120)/X hours
TIME TAKEN TO TRAVEL BY CAR : (600-120)/Y hours
120/x + 480/y = 8 (given)
⇒120Y + 480X = 8XY
⇒15Y + 60X = XY ______eqn.1( dividing each term by 8)
20 min = 20/60 hour = 1/3 hour
GIVEN : He takes 20 min longer if he travels 200 km by train and rest by car
∴ TIME TAKEN TO TRAVEL BY TRAIN : (200)/X hours
TIME TAKEN TO TRAVEL BY CAR : (600-200)/Y hours
200/X + 400/Y = 8+1/3 (∵ He takes 20 min longer )
⇒ 200/X + 400/Y = 25/3
⇒200Y + 400 X = 25XY/3 ______eqn.2
eqn.1 x 40 - eqn.2 x 3 =
600Y + 2400X = 40XY
600Y + 1200X = 25XY
( - )_____( - )_______( - )_________
0Y +1200 X = 15XY
____________________________
∴15XY = 1200X
⇒15Y =1200
⇒Y = 80
PUTTING THE VALUE OF Y = 80 IN eqn.1 WE GET :
15 x 80 + 60X = X x 80
⇒ 1200+60x=80x
⇒ 20x=1200
⇒ x=60
∴ x = 60
y = 80
∴ SPEED OF TRAIN = 60 KM/H
SPEED OF CAR = 80 KM/H
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