It took Ramon 88 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 16mph16mph and make the return drive in only 66 hours. Find his average speed on the return drive.Step 1 of 3: Complete the following table by entering the missing values, using x to represent the unknown quantity.
Question
It took Ramon 88 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 16mph16mph and make the return drive in only 66 hours. Find his average speed on the return drive.Step 1 of 3: Complete the following table by entering the missing values, using x to represent the unknown quantity.
Solution
Sure, here is the table:
| Trip | Distance | Rate | Time |
|---|---|---|---|
| To concert | d | x | 88 |
| From concert | d | x+16 | 66 |
Step 1: We know that distance = rate * time. So, we can set up the following equations based on the information given in the problem:
For the trip to the concert: d = x * 88 For the return trip: d = (x+16) * 66
Since the distance to and from the concert is the same, we can set these two equations equal to each other and solve for x:
x * 88 = (x+16) * 66
Step 2: Solve the equation for x:
88x = 66x + 1056
22x = 1056
x = 48 mph
Step 3: Substitute x = 48 mph into the equation for the return trip to find the average speed on the return trip:
d = (48+16) * 66 d = 64 * 66
So, the average speed on the return trip was 64 mph.
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