Question

A man takes 370 km path by train and apath by car if he covers 250 km by train and rest by car it takes 4 hours but if he travels130 km by train and rest by car he takes 18 minutes longer find speed of train and car

Answer 1

let speed of train is x
let speed of car is y

assume that 1/x = p
and 1/y = q

CASE 1
by speed disfance formula
x = 250 /t
then

t = 250/x
at car

y = 370-250/t' = 120/t'

t' = 120/y

given that t + t' = total time = 4 hours
thus
250/x + 120/y = 4
or
250p + 120q = 4 ………………………………… (i)

Case 2
at train
x = 130 / t"
so t"= 130 / x

at car
y = 370-130 /t''' = 240/t'''
so
t''' = 240/y

given that

t" + t''' = total time = 4 hr 18 min = 4 +18/60 hr
thus total time = 4 + 3/10 => 43/10
so
130/x + 240/y = 43/10
or
130p + 240q = 43/10
or
65p + 120q = 43/20 ………………………………… (ii)

Equation(i) - (ii) gives
185p = 4- 43/20

185p = 37/20
p = 1/100 ………………………………… (iii)
using equation (iii) in (i) gives
250/100 + 120q = 4
2.5 + 120q = 4
120q = 1.5
q = 1/ 80

as p = 1/x = 1/100 thus x= 100
as q = 1/y = 1/80 thus y =80

speed of train is 100 kmph
speed of bus is 80 kmph