Question

2) Places A and B are 100 km apart on a highway. One car starts from A and another
from B at the same time. If the cars travel in the same direction at different speeds.
they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What
are the speeds of the two cars?
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Answer 1

Answer:

Let the speed of car at A be x kmph

and the speed of car at B be y kmph

when the car travel in same direction Relative Speed is x−y

Dist=100km

t=5 hours

∴ Dist =S×T

100=(x−y)5

x−y=20⟶(I)

when car travel in opp direction Relative Speed is x+y

Dist=100km

t=1 hours

Dist=ST

100=(x+y)1

x+y=100⟶(II)

Solving (I) & (II)

x−y=20

x+y=100

2x=120

x=60km/h

y=40km/h

Speed of the car at A =60 km/h

Speed of the car at B=40 km/h

The difference of speeds is 60−40=20

Answer 2

Note- In first figure there is 1condition and in 2nd page there is 2nd condition

Solution-

Let the speed of carA be x

and speed of carB be y

Case-1

If the cars travel in the same direction at different speeds they meet in 5 hours.So we use this trick or method,

Distance travelled by carA=Speed of carA×time taken by carA=5x

Distance travelled by carB=speed of carB×time taken by carB

According to first case

$\rm 5x - 5y = 100 \\ \rm 5(x - y) = 100 \\ \rm \boxed{x - y = 20}... 1$

Case-2

If they travel towards each other, they meet in 1 hour.

Here,

Distance travelled by carA=speed of carA×time taken by carA

Distance travelled by carB=speed of carB×time taken by carB

According to second case

$\rm \boxed{x + y = 100}...2$

Using elimination method for 1st and 2nd

$\: \: \: \rm \: \: \: \: \: \: x + y = 100 \\ \boxed{ - } \rm x - y = 20 \\ - - - - - - - - \\ \rm 2y = 80 \\ \implies \rm \boxed{ y = 40}$

Here we find the speed of carB

$\rm x + y = 100 \\ \rm x + 40 = 100 \\ \rm \boxed{x = 60}$

Here we find the speed of carA

Therefore, speed of carA is 60km/hr

and speed of carB is 40km/hr