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Bill spends two days driving from Point A to Point B.

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GreenlightTestPrep
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Bill spends two days driving from Point A to Point B. [#permalink] New post   18 Dec 2018, 07:21
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Bill spends two days driving from Point A to Point B. On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?

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Bill spends two days driving from Point A to Point B. [#permalink] New post   20 Dec 2018, 07:25
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GreenlightTestPrep wrote:
Bill spends two days driving from Point A to Point B. On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?

Show: ::
35


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: 35
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Re: Bill spends two days driving from Point A to Point B. [#permalink] New post   21 Dec 2018, 10:04
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the trick here is to keep in mind that distance is the quantity that can be added.
so in order to solve the question get everything in terms of distance using the formula
speed = distance / time
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Re: Bill spends two days driving from Point A to Point B. [#permalink] New post   15 Jul 2021, 00:39
We have two clues here:
1. The time for the first part of the trip and the second part of the trip have to add up to 18 hours.
2. The distance for the first part of the trip and the second part of the trip have to add up to 680 miles.

The time for each part of the trip can be figured out using:
T2 + 2 + T2 = 18
2T2 + 2 = 18
2T2 = 16
T2 = 8

T1 + 8 = 18
T1 = 10

Since distances have to add up to 680 and D = RT:
R1 * T1 + R2 * T2 = 680
(R2 + 5) * 10 + R2 * 8 = 680
10R2 + 50 + 8R2 = 680
18R2 = 630
R2 = 35

This was a bit lengthy, but it's how I found the answer.
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Re: Bill spends two days driving from Point A to Point B. [#permalink]
15 Jul 2021, 00:39
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