Consider the following word problem:
It took Eric 10 hours to drive to a job interview. On the way home, he was able to increase his average speed by 21 mph and make the return drive in only 7 hours. Find his average speed on the return drive.
Step 1 of 3: Complete the following table by entering the missing values.
rockin a turban oh yeah oh yeah
To find Eric's average speed on the return drive, we need to first calculate his average speed on the initial drive.
Step 1: Calculate the average speed on the initial drive.
We are given that it took Eric 10 hours to drive to the job interview. Let's represent his average speed during this drive as x mph.
Distance = Speed × Time
On the initial drive:
Distance = x mph × 10 hours
To find the distance, we need the value of x. However, we don't have enough information to determine the distance or the value of x directly.
Step 2 of 3: Find the total distance of the trip.
We can find the distance by considering that the distance going to the interview and the distance returning from the interview are equal.
Distance to the interview = Distance from the interview
Using the formula from step 1, on the way home:
Distance from the interview = (x + 21) mph × 7 hours
Now we have two expressions for the distance of the trip. Setting them equal:
x mph × 10 hours = (x + 21) mph × 7 hours
Step 3 of 3: Solve for x.
Let's solve this equation to find the value of x, which represents Eric's average speed on the initial drive.
10x = 7(x + 21)
Expand the equation:
10x = 7x + 147
Simplify:
10x - 7x = 147
3x = 147
Divide both sides by 3 to isolate x:
x = 147 / 3
x = 49
Therefore, Eric's average speed on the initial drive was 49 mph.
To find his average speed on the return drive, we add 21 mph (the increase in speed):
Average speed on the return drive = Initial speed + Increase in speed
= 49 mph + 21 mph
= 70 mph
So, Eric's average speed on the return drive was 70 mph.
the distance is the same
10 (s - 21) = 7 s
10 s - 210 = 7s