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Re: Bill and Ted each competed in a 240-mile bike race. Bill’s a [#permalink]
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GreenlightTestPrep wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

Show: ::
15


Another option is to start with the following word equation:
(Bill's average speed) + 5 = (Ted's average speed) [since Bill’s average speed was 5 miles per hour slower than Ted’s average speed]

Let t = Bill's travel TIME (in hours)
So, t - 4 = Ted's travel TIME (in hours) [since Ted completed the race 4 hours sooner than Bill did]

speed = distance/time

So, our word equation becomes: 240/t + 5 = 240/(t - 4)
Multiply both sides by t to get: 240 + 5t = 240t/(t - 4)
Multiply both sides by (t - 4) to get: 240(t - 4) + 5t(t - 4) = 240t
Expand: 240t - 960 + 5t² - 20t = 240t
Subtract 240 t from both sides: -960 + 5t² - 20t = 0
Rearrange: 5t² - 20t - 960 = 0
Divide both sides by 5 to get: t² - 4t - 192 = 0
Factor to get: (t - 16)(t + 12) = 0

So, EITHER t = 16 OR t = -12

Since the time cannot be NEGATIVE, we can conclude that t = 16
In other words, Bill's travel time was 16 hours

What was Bill’s average speed in miles per hour?
speed = distance/time
So, Bill's speed = 240/16 = 15 miles per hour

Answer: 15

Cheers,
Brent
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Re: Bill and Ted each competed in a 240-mile bike race. Bill’s a [#permalink]
2
GreenlightTestPrep wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?

Show: ::
15


As I mention in the video below, these kinds of questions can be solved in a variety of ways.

For our 3rd approach, let's start with a word equation involving distances traveled.
Since Bill and Ted both traveled 240 miles, we can write:
Bill's travel distance = Ted's travel distance

Let x = Bill's speed
So, x + 5 = Ted's speed

Let t = Ted's travel time (in hours)
So, t + 4 = = Bill's travel time (in hours)

Distance = (speed)(time)
Plug values into the word equation to get: (x)(t + 4) = (x + 5)(t)
Expand to get: xt + 4x = xt + 5t
Subtract xt from both sides to get: 4x = 5t
Divide both sides by 5 to get: 4x/5 = t

Where do we go from here?

Well, we know that Bill traveled 240 miles
So, (Bill's speed)(Bill's travel time) = 240
In other words: (x)(t + 4) = 240
Replace t with 4x/5 to get: (x)(4x/5 + 4) = 240
Expand: 4x²/5 + 4x = 240
Multiply both sides by 5 to get: 4x² + 20x = 1200
Divide both sides by 4 to get: x² + 5x = 300
Rewrite as: x² + 5x - 300 = 0
Factor: (x - 15)(x + 20) = 0
So, EITHER x = 15 OR x = -20
Since the speed cannot be negative, it must be the case that x = 15

Answer: 15

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Re: Bill and Ted each competed in a 240-mile bike race. Bill’s a [#permalink]
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Re: Bill and Ted each competed in a 240-mile bike race. Bill’s a [#permalink]
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