First recognize that we have TWO pieces of information regarding the time Bill spent driving each day.
On day 1, Bill drove 2 hours longer than he drove on day 2.
So, let x = # of driving hours on day 2
Then x + 2 = # of driving hours on day 1

Bill drove a TOTAL of 18 hours
So, x + (x + 2) = 18
Simplify: 2x + 2 = 18
Solve, x = 8
So, Bill drove 10 hours on day 1 and he drove 8 hours on day 2

Now let's solve the question by starting with a word equation.
Let x = speed driven on day 2
So, x + 5 = speed driven on day 1

(Distance traveled on day 1) + (Distance traveled on day 2) = 680
Distance = (rate)(time)
We get: (x+ 5)(10) + (x)(8) = 680
Expand: 10x + 50 + 8x = 680
Simplify: 18x + 50 = 680
18x = 630
x = 35 (mph)

Answer:

Cheers,
Brent

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10 (x+5) + 8x = 680

Solve for X = 35

Explanation:

Lets say he drove at X mi/hr on second day and he drove for Y hours

Question says he drove 2 hrs extra on day 1 so day 1 hours = Y + 2

Speed on day 1 is 5 mi/hr faster so, speed on day 1 = x + 5

Total time he drove (Day 1 + Day 2) = 18

Y + (Y+2) = 18

Y = 8 (Second day's time)

Y + 2 = 10 (First day's time)

Total distance covered = 680 = Speed of day 1* time for day + Speed of day2* time of day2

Putting values we get the very first equation.

HTH

Forma table -


2T + 2 = 18

So, 2T = 16

Or, t = 8


Now, 10s + 50 + 8s = 680

Or, 18s = 630

Or, s = 35

Hence, average speed on day 2 was 35, answer will be (E)...
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We are given that on the first day, Bill drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. We can let the rate on the second day = r and the rate on the first day = r + 5. Also, we can let the time on the second day = t and the time on the first day = t + 2.

Since the total time is 18, we can create the following equation to determine t:

t + t + 2 = 18

2t = 16

t = 8

Thus, the distance on day 2 is 8r and the distance on day 1 is (r + 5)(10) = 10r + 50

We can create the following equation to determine r:

8r + 10r + 50 = 680

18r = 630

r = 35

Answer: E
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I'm probably confusing formulas, but aren't you allowed to "add rates" together?

I had created the formula

(2s+5) x 18 = 680
Clearly got the wrong answer but hoping someone can refresh me onto a strategy that shouldn't be used for this!

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