Two cars, A and B are traveling at speeds 90km/h and 45km/h respectively. If A is 15 km behind B. Assuming they maintain the same speeds, how long will it take (in minutes) for A to overtake B?
Let's assume that it takes time "t" hours for car A to overtake car B.
The distance traveled by car A in time "t" hours is: 90t
The distance traveled by car B in time "t" hours is: 45t
As given, A is 15 km behind B, so we can set up the equation:
90t = 45t + 15
Simplifying the equation, we get:
45t = 15
Dividing by 45 on both sides of the equation:
t = 15/45
t = 1/3 hours
Converting hours to minutes:
In 1 hour, there are 60 minutes.
So, in 1/3 hour, there are (1/3) * 60 = 20 minutes.
Therefore, it will take 20 minutes for car A to overtake car B.
To determine the time it will take for Car A to overtake Car B, we need to calculate the time it will take for Car A to cover the distance between them. Let's break it down step-by-step:
Step 1: Convert the speeds from km/h to km/min.
Car A's speed = 90 km/h = 90 km / 60 min = 1.5 km/min
Car B's speed = 45 km/h = 45 km / 60 min = 0.75 km/min
Step 2: Calculate the relative speed between the two cars.
Relative speed = Car A's speed - Car B's speed
Relative speed = 1.5 km/min - 0.75 km/min = 0.75 km/min
Step 3: Calculate the time it will take for Car A to cover the distance of 15 km.
Time = Distance / Relative speed
Time = 15 km / 0.75 km/min = 20 min
Therefore, it will take 20 minutes for Car A to overtake Car B.
To find out how long it will take for car A to overtake car B, we can use the formula:
Time = Distance / Relative Speed.
First, let's determine the relative speed between car A and car B. Since car A is traveling at 90 km/h and car B is traveling at 45 km/h, the relative speed will be the difference between their speeds:
Relative Speed = Speed of A - Speed of B = 90 km/h - 45 km/h = 45 km/h.
Next, we need to calculate the distance that car A needs to cover to catch up to car B. Given that A is 15 km behind B, car A needs to cover this distance:
Distance = 15 km.
Now, we can use the formula to find the time it will take for car A to overtake car B:
Time = Distance / Relative Speed = 15 km / 45 km/h.
To convert this time to minutes, we need to multiply it by 60 since there are 60 minutes in an hour:
Time = (15 km / 45 km/h) * 60 minutes/hour.
Simplifying the equation:
Time = 15 km / 0.75 km/minute = 20 minutes.
Therefore, it will take 20 minutes for car A to overtake car B.