You drive to the store at 20 mph and return by the same route at 30 mph. Ignoring the time spent at the store, what was your average speed?
let the distance to the store be x miles
time for first trip = x/20
time for second trip = x/30
total time = x/20 + x/30 = x/12
avg speed = total distance/total time
= 2x/(x/12)
= 2x(12/x) = 24 mph
To find the average speed, we need to calculate the total distance traveled and the total time taken.
Let's start by finding the total distance traveled. Since the distance to the store and back is the same (since it's the same route), we can consider it as 2 times the distance to the store.
Let's assume the distance to the store is "d" miles.
So, the total distance traveled is 2d miles.
Next, we need to find the total time taken. We know the speed at which you drove to the store was 20 mph, and the speed at which you returned was 30 mph. Since the time taken is inversely proportional to the speed (i.e., the higher the speed, the less time it takes), we can calculate the time taken using the formula: time = distance / speed.
The time taken to drive to the store (one way) is d / 20 hours.
The time taken to return from the store (one way) is d / 30 hours.
To find the total time taken, we add both the times: d / 20 + d / 30 hours.
Now, to find the average speed, we divide the total distance traveled by the total time taken:
Average Speed = Total distance / Total time
= 2d / (d / 20 + d / 30) mph
To simplify this expression, we need to find a common denominator for the fractions in the denominator:
Average Speed = 2d / [(3d + 2d) / (60d)] mph
= 2d * (60d) / (3d + 2d) mph
= (120d^2) / (5d) mph
= 24d mph
So, the average speed is 24d mph.
Please note that the value of "d" is not given in the question, so the average speed in terms of "d" represents the general formula. If you have a specific value for "d," you can substitute it to find the numerical value.