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Answer :
Final answer:
The driver catches up with the pedestrian in 60 minutes by calculating the relative speed (36 mph) and then using the time formula (Time = Distance / Relative Speed) to get the time required. The correct option is B.
Explanation:
To find out how long it takes the driver to catch up with the pedestrian, we must calculate the time it takes for the driver, to travel at a speed faster than the pedestrian, to cover the distance between them.
The pedestrian is initially 4 miles ahead and moves at 4 mph, and the driver moves at 40 mph. First, we calculate the relative speed of the driver concerning the pedestrian. The relative speed is the difference in their speeds because they are moving in the same direction.
Relative Speed = Speed of Driver - Speed of PedestrianRelative Speed = 40 mph - 4 mphRelative Speed = 36 mph
Now that we have the relative speed, we can calculate the time it takes for the driver to catch up with the pedestrian using the formula:
Time = Distance / Relative SpeedTime = 4 miles / 36 mph
Converting miles per hour to miles per minute by dividing by 60:
Relative Speed = 36 mph / 60Relative Speed = 0.6 miles/minute
Now, we calculate the time:
Time = 4 miles / 0.6 miles/minute time = 6.67 minutes.
To convert the time from minutes to hours, multiply by 60:
Time (minutes) = 6.67 minutes * 60Time (minutes) = 400 minutes
Therefore, the correct time it takes the driver to catch up with the pedestrian is 60 minutes.
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