Question

points A and B are 70 km apart on a highway. a car starts from A and another car starts from B at same direction they meet in 7 hrs but if they travel towards each other they meet in 1 hr. what are there speed

Answer 1

$Hi \: \: there \\ \\ let \: X \: and \: Y \: be \: the \: two \: cars \: starting \: from \\ \\ each \: from \: points \: A \: and \: B \: respectively , \: let \: they \: have \\ \\ \: speed \: of \: x km \: /h \: \\ and \: y \: km \: /h \: respectively \\ \\ CASE \: :- \: 1 \\ \\ When \: two \: cars \: moves \: in \: the \: same \: directions - \\ \\ \: lets \: assume \: that \: two \: cars \: meet \: at \: same \: point \: Q \\ \\ \: Distance \: travelled \: by \: car \: X = \: AQ \\ \\ \: Distance \: Travelled \: by \: Car \: Y = \: BQ \\ \\ \: Given \: that \: two \: cars \: meet \: in \: 7hrs \\ \\ Distance \: travelled \: by \: car \: X \: in. \: 7 \: hours = \: 7x km \\ \\ \: AQ = \: 7x \\ \\ similarly \: , BQ = 7y \\ \\ eventually , AB = AQ - BQ \\ \\ => AB = 7x - 7y = 70 \\ \\ => AB = x - y = 10 ..... ( 1 ) \\ \\ By \: solving \: [ \: See \: attached \: pic \: for \: solution ] \\ \\ \\ CASE :- \: ( 2 ) \: when \: \: two \: cars \: move \: in \: opposite \: to \: each \: other \\ \: suppose \: they \: meet \: in \: point \: P \\ \\ then \: Distance \: travelled by \: Car \: X = \: AP \\ \\ Distance \: Covered \: by \: Car \: Y = \: BP \\ \\ In \: this \: case \: cars \: meet in \: 1 hr . \\ \: so , \: Car \: X = x \\ \\ car \: y = y \\ clearly \\ \: \\ \\ AP + BP = AB \\ \\ => x + y = 70 \: \\ by \: solving \: these \: two \: equation \: (see \: attached \: pic \: ) \\ \\ speed \: of \: car \: x \: \: \: = 40km {h}^{ - 1} \\ \\ and \: car \: y \: = 30 \: km {h}^{ - 1}$
Hope this helps ya ☺

Answer 2

Hey.....!!! :)) ✌️✌️

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Let the speed of the car at point A be X km / h
let the speed of the car at point B be Y km/h

The respective speed of the car when they are traveling in the same direction is = X - Y

Given,

Step 1 :- they travel in some direction and meet after 7 hours

Distance between the points = 70 km / h


=> 7 ( X - Y ) = 70

:- X- Y = 10 ...... ( i )

Step 2 :- they travel in opposite directions and meet after 1 hours

:-. 1 ( X+ Y ) = 70 .... (ii)

solving equations (i) or (ii)

X - Y = 10
X + Y = 70
(+) (+) (+)
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2 X = 80
X = 80 / 2
=> X = 40
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Than
Y = 30

X = 40 km/ h

Y = 30 km/ h Ans.

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I hope it's help you.....!!! :)) ✌️✌️