Two cars travel westward along a straight highway, one at a constant velocity of 74 km/h, and the other at a constant velocity of 108 km/h.
(a) Assuming that both cars start at the same point, how much sooner does the faster car arrive at a destination 6 km away?
To find out how much sooner the faster car arrives at the destination, we need to calculate the time it takes for both cars to travel the same distance.
Let's start by determining the time it takes for each car to travel 6 km.
For the slower car:
Time = Distance / Velocity
Time = 6 km / 74 km/h
To calculate this, we divide the distance of 6 km by the velocity of 74 km/h:
Time = 6 km / 74 km/h = 0.0811 hours
For the faster car:
Time = Distance / Velocity
Time = 6 km / 108 km/h
Similarly, we divide the distance of 6 km by the velocity of 108 km/h:
Time = 6 km / 108 km/h = 0.0556 hours
To find out how much sooner the faster car arrives, we subtract the time it takes for the slower car from the time it takes for the faster car:
Time difference = Time of faster car - Time of slower car
Time difference = 0.0556 hours - 0.0811 hours
Now we calculate the time difference:
Time difference = -0.0255 hours
The negative sign indicates that the slower car arrives first. So, the faster car arrives 0.0255 hours later than the slower car.
To convert this time to minutes, we multiply it by 60 since there are 60 minutes in an hour:
Time difference in minutes = -0.0255 hours * 60 = -1.53 minutes
Therefore, the faster car arrives approximately 1.53 minutes later than the slower car.