Question

23. Points A and B are 70 km apart on a highway. 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 h, but if they travel towards each other they meet in
'1 h. What are the speeds of the cars?​

Answer 1

Step-by-step explanation:

7x-7y=70

x+y=70

x=40km/h

y=30km/h

Answer 2

$\large\underline\pink{Given:-}$

• Points A and B are 70 km apart on a highway. 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 h, but if they travel towards each other they meet in '1 h.

$\large\underline\pink{To find:-}$

• Fine the speeds of the car ....?

$\large\underline\pink{Solutions:-}$

• Let the speed of car at A be x km/hr and the speed of car at B be y km/hr.

Distance cover by car A in 1 hr = x km

Distance cover by car B in 1 hr = y km

x + y = 70 _______(i).

Distance travelled by car A in 7 hr = 7x km

Distance travelled by car B in 7 hr = 7y km

7x - 7y = 70

x - y = 10 _________(ii).

Now, Solving the Eq. (ii) and (i). we get,

${x} \: + \: {y} \: \: = \: \: {70} \\ {x} \: - \: {y} \: \: = \: \: {10} \\ \underline{- \: \: \: \: \: \: + \: \: = \: \: \: - \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: {2y} \: \: \: \: \: = \: \: \: {60}$

$\: \: \: \: \: \leadsto \: \: y \: \: = \: \: \frac{60}{2}$

$\: \: \: \: \: \leadsto \: \: y \: \: = \: \: {30}$

Now, putting the value of y in Eq. (i)

$\: \: \: \: \: \leadsto \: \: {x} \: + \: {y} \: \: = \: \: {70}$

$\: \: \: \: \: \leadsto \: \: {x} \: + \: {30} \: \: = \: \: {70}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {70} \: - \: {30}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {40}$

Hence, the speed of car x and y is 40 km/hr and 30 km/hr.