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Joined: 10 Apr 2015
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Bill and Ted each competed in a 240-mile bike race. Bill’s a
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06 Jun 2017, 13:00
06 Jun 2017, 13:00
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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?
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15
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Bill and Ted each competed in a 240-mile bike race. Bill’s a
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07 Jun 2017, 15:11
07 Jun 2017, 15:11
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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?
Bill’s average speed was 5 miles per hour slower than Ted’s average speed.
Let B = Bill's travel speed
So, B + 5 = Ted's average speed
Ted completed the race 4 hours sooner than Bill did
Let's start with a word equation:
(Bill's travel time) = (Ted's travel time) + 4
time = distance/speed
So, we get: 240/B = 240/(B + 5) + 4
Rewrite 4 as 4(B + 5)/(B + 5) to get: 240/B = 240/(B + 5) + 4(B + 5)/(B + 5)
Simplify: 240/B = 240/(B + 5) + (4B + 20)/(B + 5)
Combine terms: 240/B = (4B + 260)/(B + 5)
Cross multiply: 240(B + 5) = (B)(4B + 260)
Expand and simplify: 240B + 1200 = 4B² + 260B
Set equal to zero: 4B² + 20B - 1200 = 0
Divide both sides by 4 to get: B² + 5B - 300 = 0
Factor: (B + 20)(B - 15) = 0
So, EITHER B = -20 OR B = 15
Since B (Bill's speed) cannot be a negative value, we can conclude that B = 15.
Answer: 15
Target Test Prep Representative
Joined: 09 May 2016
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Re: Bill and Ted each competed in a 240-mile bike race. Bill’s a
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05 Dec 2017, 18:19
05 Dec 2017, 18:19
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Expert Reply
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
We are given that Bill and Ted each competed in a 240-mile bike race. We are also given that Bill’s average speed was 5 miles per hour slower than Ted’s average speed.
Both Bill and Ted had distance of 240 miles. If we let Ted’s speed = r, we can let Bill’s speed = r - 5. We can use the above information to determine the time of Bill and Ted in terms of variable r.
Since time = distance/rate, Ted’s time = 240/r and Bill’s time = 240/(r - 5).
Since Ted completed the race 4 hours sooner than Bill did, we can create the following equation:
240/r + 4 = 240/(r - 5)
To eliminate the denominators of the fractions we can multiply the entire equation by r(r-5) and we have:
240(r - 5) + 4[r(r - 5)] = 240r
240r - 1,200 + 4r^2 - 20r = 240r
4r^2 - 20r - 1,200 = 0
r^2 - 5r - 300 = 0
(r - 20)(r + 15) = 0
r = 20 or r = -15
Since r must be positive, r = 20.
Thus, Bill’s rate = 20 - 5 = 15 mph.
