Respuesta :
Answer:
Two cars are 400 km apart. One car is traveling at 55 km/h and the other car is traveling at 45 km/h if they start at the same time and are driving toward each other, the two cars will meet after 4 hours .
Solution:
Let the two car be A and B.
Given that two cars are 400 km apart.
Let us assume distance travelled by A to meet B = x km
The distance travelled by B can be found out by subtracting the total distance x from distance travelled by A.
So distance travelled by B = (400-x) km
Time taken will be same for A and B
We know that, [tex]\text\bold{ {Speed}=\frac{\text {Distance}}{\text {Time}}}[/tex]
So, we get
[tex]\text { Time }=\frac{\text { Distance }}{\text { speed }}[/tex]
Let us consider the time taken by car [tex]A=T_{A}[/tex] .So time taken by A to travel x km =[tex]\frac{x}{55}[/tex]
Similarly, time taken by B to travel distance (400-x) km = [tex]T_{B}=\frac{400-x}{45}[/tex]
When the two cars meet, [tex]\bold{\mathrm{Ta}=\mathrm{Tb}}[/tex].hence we get,
[tex]\frac{x}{55}=\frac{400-x}{45}[/tex]
On solving above equation,
[tex]\frac{x}{55}=\frac{400-x}{45}[/tex]
[tex]\frac{x}{11}=\frac{400-x}{9}[/tex]
9x = 11(400 – x)
9x = 4400 – 11x
9x + 11x = 4400
20x = 4400
X = 220
After 220 km of travel, the car with speed of 55 km will meet other car travelling with speed of 45 km. now the time taken for two cars to meet each other is given as,
Time taken for cars to meet = [tex]\frac{220}{55}=4[/tex]
Hence the two cars will meet after 4 hours.
