Question

a car traveling at 48 mph overtakes a cyclist who, riding at 12 MPH has a 3 hour head start. how far from the starting point does the car overtake the cyclist.

Answer 1

Let's first find out how far the cyclist has traveled in 3 hours at a speed of 12 mph:

distance = speed x time
distance = 12 mph x 3 hours
distance = 36 miles

So, the cyclist has traveled 36 miles in 3 hours.

Now, let's find out how long it takes for the car to catch up to the cyclist:

Let t be the time it takes for the car to catch up to the cyclist.

distance traveled by car = distance traveled by cyclist + 36 miles (the head start distance).

Using the formula distance = speed x time, we can express the distance traveled by the car and the cyclist as follows:

distance traveled by car = 48 mph x t
distance traveled by cyclist = 12 mph x t

We can now set up the equation:

48t = 12t + 36

Simplifying the equation:

48t - 12t = 36

36t = 36

t = 1 hour

Therefore, it takes 1 hour for the car to catch up to the cyclist.

To find the distance from the starting point where the car overtakes the cyclist, we can substitute t = 1 hour in the formula:

distance traveled by car = 48 mph x 1 hour = 48 miles

So, the car overtakes the cyclist at a distance of 48 miles from the starting point.