Answer

Verified

355.9k+ views

Hint: If the cars move in the same direction, they would take longer to meet each other. If they start from opposite directions, they would meet much faster. Further, in addition to this, we would use the formula below to find the speed of a car-

$speed=\dfrac{dis\tan ce}{speed}$

Complete step-by-step solution:

Let the speed of the car at A be A$\dfrac{km}{hr}$ and the other car at B be B$\dfrac{km}{hr}$. Now, from first condition (for cars going in same direction)-

Let car at A cover distance x km and car at B cover distance y km in duration of 9 hours (time when they meet). We have,

Distance = speed$\times $time

x = A$\times $9

y = B$\times $9

Now, since cars at A and B are 90 km apart and finally after 9 hours, they finally meet, car A would have to cover 90 km more than B since they travel in the same direction. Thus,

x = y+90

Plugging values of x and y,

9A=9B+90

A=B+10 -- (1)

From second condition (for cars going in opposite direction)-

Let a car at A cover distance x km and car at B cover distance y km in duration of $\dfrac{9}{7}$ hours (time when they meet). We have,

Distance = speed$\times $time

x = A$\times $ $\dfrac{9}{7}$

y = B$\times $$\dfrac{9}{7}$

Now, since cars at A and B are 90 km apart and finally after $\dfrac{9}{7}$ hours they meet, since they are travelling in opposite directions, the total distance covered by cars is 90 km. Thus,

x+y=90

A$\times $ $\dfrac{9}{7}$+ B$\times $$\dfrac{9}{7}$=90

$\dfrac{A+B}{7}$=10

A+B=70 -- (2)

Adding (1) and (2),

2A = 80

A=40$\dfrac{km}{hr}$

Putting this value in (2),

We get, B=70-A

B=30$\dfrac{km}{hr}$

Hence, the car A has a speed of 40kmph and B has a speed of 30kmph

Note: We can solve this problem by using the concept of relative speeds. Thus, if cars move in the same directions, we subtract the speeds. While the cars move in the opposite directions, we add the speeds. In this case, we use the distance as 90 km. Now, for same directions, we have,

Speed of car at A is A$\dfrac{km}{hr}$ and at B is B$\dfrac{km}{hr}$

Distance = speed$\times $time

90 = (A-B)$\times $9 (Since, they meet after 9 hours)

(A-B) = 10

A=B+10 -- (a)

Similarly, for cars travelling in opposite directions, we add the speeds, we would have,

90 = (A+B) $\times $ $\dfrac{9}{7}$

(A+B) = 70 -- (b)

Thus, we get the same equations((a) and (b)) as (1) and (2) in the solution described above. So, we would get the same answers for speeds of car at A and car at B.

Thus, we would get the same answer for A and B as we got in the solution.

$speed=\dfrac{dis\tan ce}{speed}$

Complete step-by-step solution:

Let the speed of the car at A be A$\dfrac{km}{hr}$ and the other car at B be B$\dfrac{km}{hr}$. Now, from first condition (for cars going in same direction)-

Let car at A cover distance x km and car at B cover distance y km in duration of 9 hours (time when they meet). We have,

Distance = speed$\times $time

x = A$\times $9

y = B$\times $9

Now, since cars at A and B are 90 km apart and finally after 9 hours, they finally meet, car A would have to cover 90 km more than B since they travel in the same direction. Thus,

x = y+90

Plugging values of x and y,

9A=9B+90

A=B+10 -- (1)

From second condition (for cars going in opposite direction)-

Let a car at A cover distance x km and car at B cover distance y km in duration of $\dfrac{9}{7}$ hours (time when they meet). We have,

Distance = speed$\times $time

x = A$\times $ $\dfrac{9}{7}$

y = B$\times $$\dfrac{9}{7}$

Now, since cars at A and B are 90 km apart and finally after $\dfrac{9}{7}$ hours they meet, since they are travelling in opposite directions, the total distance covered by cars is 90 km. Thus,

x+y=90

A$\times $ $\dfrac{9}{7}$+ B$\times $$\dfrac{9}{7}$=90

$\dfrac{A+B}{7}$=10

A+B=70 -- (2)

Adding (1) and (2),

2A = 80

A=40$\dfrac{km}{hr}$

Putting this value in (2),

We get, B=70-A

B=30$\dfrac{km}{hr}$

Hence, the car A has a speed of 40kmph and B has a speed of 30kmph

Note: We can solve this problem by using the concept of relative speeds. Thus, if cars move in the same directions, we subtract the speeds. While the cars move in the opposite directions, we add the speeds. In this case, we use the distance as 90 km. Now, for same directions, we have,

Speed of car at A is A$\dfrac{km}{hr}$ and at B is B$\dfrac{km}{hr}$

Distance = speed$\times $time

90 = (A-B)$\times $9 (Since, they meet after 9 hours)

(A-B) = 10

A=B+10 -- (a)

Similarly, for cars travelling in opposite directions, we add the speeds, we would have,

90 = (A+B) $\times $ $\dfrac{9}{7}$

(A+B) = 70 -- (b)

Thus, we get the same equations((a) and (b)) as (1) and (2) in the solution described above. So, we would get the same answers for speeds of car at A and car at B.

Thus, we would get the same answer for A and B as we got in the solution.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE