Question

Question for mods only


The distance between two places A and B on a road is 70 kilometres. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other they meet in one hour. What are their speeds?​

Answer 1

$\red{ \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  COMPLETE \: \: QUESTION \:   \maltese }}}}}$

• The distance between two places A and B on a road is 70 kilometres. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other they meet in one hour. What are their speeds?

$\Large\green{\qquad\underline{\pmb{{ \mathbb { \maltese  \:  Here\:  \maltese }}}}}$

$\purple{\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  REQUIRED \: \: INFO \:  \maltese }}}}}$

$\Large \orange{\qquad \underline{ \pmb{{ \mathbb{ \maltese  \:SOLUTION \:  \maltese }}}}}$

$\huge\fbox\pink{✯consider✯}$

• Let the speed of the car starting from A be x km/h and that of the car starting from B be y km/h

$\large \mathfrak{ \text{W}e \: \text{K}now }$

The distance between the two car is 70 KM.

if they travel in the same direction they meet 7 hour .

$\huge\fbox\pink{✯Therefore ✯}$

The distance travelled by the car starting from A

in 7 hours =7x km (distance =Speed ×time) and that by the car from B = 7y km.

$\color{magenta}\huge\mathfrak{  \text{H}ence \:   \: Proved}$

• 7x-7y = 70 (the car starting from A has covered 70 KM more)

• x-y = 10 (1)

If they travel towards each other, the total distance travelled by them will be 70 km.

▬▬▬▬▬▬▬▬▬▬▬▬

In one hour the distance travelled by the car starting from A = x km and that by the car from B = y km

• x+y = 70 (2)

Adding equation (1) and (2) we get

• x-y = 10 (1)

• + x+y = 70 (2)
• -------------------------
• 2x = 80

$\huge\fbox\pink{✯Therefore ✯}$

• x = 80 /2

• x = 40

Put x = 40 in equation (2)

• 40 +y = 70

• y=70 - 40

• y= 30

$\huge\fbox\pink{✯Final Answer✯}$

• The speed of the car starting from A and B are 40 km / h and 30 km/ h respectively.

$\huge\boxed{\dag\sf\red{Thanks}\dag}$

Answer 2

Answer:

When they travel in same direction, suppose

they meet when B travels for x m, then A will have travelled 70+x

m in the same time

Since, Speed =

Time

Distance

Speed of car at A =

7

x+70

And Speed of car at B =

7

x

And when they travel in the opposite direction, suppose they meet when A

travels for y m, then B will have travelled 70−y m in the same

time

Speed of car at A =

1

y

=y

And Speed of car at B =

1

70−y

=70−y

Equating the speeds of the cars in both the cases,

Speed of car at A,

7

x+70

=y

x+70=7y

=>x−7y=−70 --- (1)

Speed of car at B,

7

x

=70−y

=>x+7y=490 --- (2)

Adding equations 1 and 2, we get 2x=420=>x=210

So, Speed of car at A =

7

x+70

=

7

280

=40km/hr

Speed of car at B =

7

x

=

7

210

=30km/hr