Two cars travel in the same direction along a straight highway, on at a constant speed of 38.0 mi/h and the other at 89.0 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 44.0 mi away? (b) How far must the faster car travel before it has a 14.0-min lead on the slower car? (The faster car is far enough ahead, that it will take the slower car 14.0-min to cover this distance.)
a. 38 * t1 = 44 mi.
Solve for t1.
89*t2 = 44. Solve for t2.
T = t1-t2
b. d = 38(14/60) = 8.9 mi.
To solve this problem, we need to use the basic formula: Distance = Speed × Time. We will use this formula to calculate the time taken by each car to cover the given distances.
a) To find out how much sooner the faster car arrives at a destination 44.0 mi away, we will divide the distance by the speed of each car and compare the times taken.
The slower car travels at a speed of 38.0 mi/h, so the time taken for it to cover a distance of 44.0 miles is:
Time taken by slower car = Distance / Speed
Time taken by slower car = 44.0 mi / 38.0 mi/h
The faster car travels at a speed of 89.0 mi/h, so the time taken for it to cover a distance of 44.0 miles is:
Time taken by faster car = Distance / Speed
Time taken by faster car = 44.0 mi / 89.0 mi/h
We can now calculate the time difference between the two cars:
Time difference = Time taken by slower car - Time taken by faster car
b) To find out how far the faster car must travel before it has a 14.0-min lead on the slower car, we will first convert the lead time to hours. There are 60 minutes in an hour, so 14.0 minutes is equal to 14.0/60 = 0.23 hours.
Now, we can set up an equation based on the time difference between the two cars:
Time taken by faster car - Time taken by slower car = 0.23 hours
We will use the same formula as before to calculate the time taken by each car, but this time we will keep the distance as the unknown:
Time taken by slower car = Distance / Speed (slower car)
Time taken by faster car = (Distance - unknown distance) / Speed (faster car)
Substituting these values into the equation:
(Distance - unknown distance) / Speed (faster car) - Distance / Speed (slower car) = 0.23 hours
We can solve this equation to find the unknown distance traveled by the faster car.