a man travels 700km partly by train and by car if he travels 250 km by train and rest by - Maths -

Question

a man travels 700km partly by train and by car if he travels 250
km by train and rest by car he takes 4 hrs but if he travels 130 by
train and rst bycar he takes 18 mins longer find the speed of the
train and the car

Ajanta Trivedi · Accepted Answer

let the speed of the train and car be x km/hr and y km/hr respectively.

total distance = 700 km.

if he travels 250 km by train , the remaining distance covered by car = 700-250 = 450 km

time taken = 4 hrs

time = distance / speed

therefore

$\frac{250}{x} + \frac{450}{y} = 4$ ......................(1)

if he travels 130 km by train , the remaining distance to covered = 700-130 = 570 km

time taken to travel = 4 hrs + 18 min = $4 \frac{18}{60} h r = 4 \frac{3}{10} = \frac{43}{10} h r s$

therefore

$\frac{130}{x} + \frac{570}{y} = \frac{43}{10} ........... (2)$

put 1/x = u and 1/y = v in eq(1) and eq(2):

$250 u + 450 v = 4 \Rightarrow 125 u + 225 v = 2............ (3) 130 u + 570 v = \frac{43}{10} ............ (4)$

multiplying eq(3) by 26 and eq(4) by 25 and then subtracting:

$3250 u + 5850 v = 52 3250 u + 14250 v = 107.5 - 8400 v = - 55.5 v = \frac{55.5}{8400} = \frac{555}{84000} = \frac{37}{5600}$

therefore y = 1/v = 5600/37 km/hr

and put the value of y in eq(1) to find the value of x.

hope this helps you.

cheers!!

a man travels 700km partly by train and by car.if he travels 250 km by train and rest by car he takes 4 hrs.but if he travels 130 by train and rst bycar he takes 18 mins longer find the speed of the train and the car