It took Eric 8 hours to drive to a job interview. On the way home, he was able to increase his average speed by 18mph and make the return drive in only 5 hours. Find his average speed on the return drive.
Rate x time =distance
Original drive- x. ____ _____
Return drive- ____ ____ _____
Let's assume Eric's average speed on the original drive is "x" mph.
On the original drive, the time is 8 hours, so we have:
8 hours * x mph = distance
On the return drive, Eric increased his average speed by 18 mph, so his new average speed is "x + 18" mph.
On the return drive, the time is 5 hours, so we have:
5 hours * (x + 18) mph = distance
Since the distance is the same for both drives, we can set the two equations equal to each other:
8x = 5(x + 18)
Expanding the equation:
8x = 5x + 90
Subtracting 5x from both sides:
3x = 90
Dividing both sides by 3:
x = 30
Therefore, Eric's average speed on the return drive is:
x + 18 = 30 + 18 = 48 mph
To find Eric's average speed on the return drive, we can use the formula:
Average speed = distance / time
Step 1: Calculate the distance of the original drive.
Since Eric traveled at a certain average speed for 8 hours, we can use the formula:
Distance = average speed * time
Let's say the average speed of the original drive is "x". Therefore, the distance of the original drive is:
Distance = x * 8
Step 2: Calculate the distance of the return drive.
Since Eric traveled at an increased average speed for 5 hours, we can use the same formula:
Distance = average speed * time
Let's say the average speed of the return drive is "x + 18". Therefore, the distance of the return drive is:
Distance = (x + 18) * 5
Step 3: Set up an equation using the distances from steps 1 and 2.
Since the total distance traveled is the same, we can set up an equation to find "x" by equating the two distances:
x * 8 = (x + 18) * 5
Step 4: Solve for "x".
Start by distributing 5 to (x + 18):
8x = 5x + 90
Next, combine like terms:
8x - 5x = 90
3x = 90
Divide both sides by 3:
x = 30
Step 5: Calculate Eric's average speed on the return drive.
Now that we know "x" is 30 mph, we can calculate the average speed of the return drive by adding 18 to it:
Average speed = 30 + 18
Average speed = 48 mph
Therefore, Eric's average speed on the return drive was 48 mph.
let the distance driven be x km
speed on first leg = x/8
speed on return leg = x/8 + 18 km/h
= (x + 144)/8 km/h
distance/rate = time
x/((x+144)/8) = 5
8x/(x+144) = 5
8x = 5x + 144
3x = 144
x = 48
so speed on return trip
= (48+144)/8 km/h
= 24 km/h