HELP ME The distance between two cities A and B is 140 km. A car driving from A to B left at the same time as a car driving from B to A. The cars met after one hour, then the first car reached city B 35 minutes later than the second car reached city A. Find the speed of the car from city A to B. *
A. 60 km/h
B. 50 km/h
C. 80 km/h
D. 70 km/h

The correct option is;

B. 50 km/h

Step-by-step explanation:

The information given in the question are;

The distance between the two cities = 140 km

The direction of motion of the first car = From A to B (left)

The direction of motion of the second car = From B to A

The time after which both cars meet = 1 hour

The time duration it takes after both cars meet for the second car to reach A = 35 minutes

The total time taken by the second car from city B to city A = The time it takes to meet the first car + The time it takes after meeting the first car to reach city A

∴ The total time taken by the second car from city B to city A = 1 hour + 35 minutes = 60 minutes + 35 minutes = 95 minutes

95 minutes = 95/60 hours = 1⁷/₁₂ hours =  1.58 hours

The speed of the second car = Distance/Time = 140 km/(1.58 hours) ≈ 88.42 km/h

Therefore, let the distance from A of the point the first car meet the second car = x

Therefore, we have;

The distance from B of the point both cars meet  = (140 - x) km

Given that both cars meet after one hour, we have;

The distance travelled by the second car coming from city B, after one hour = (140 - x) km = Speed of the second car × 1 hour

88.42 km/h × 1 hour = 88.42 km = (140 - x) km

x = 140 - 88.42 ≈ 51.58 km

The distance from A of the point the first car meet the second car = x = 51.58 km

The speed of car A = (The distance from A of the point the first car meet the second car)/(Time it takes both cars to meet)

∴ The speed of the first car = 51.58 km/(1 hour)

The speed of the first car = 51.58 km/h ≈ 50 km/h (Rounding up to the nearest 10th).

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: