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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?

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?

A) 7.5 B) 10 C) 12 D) 12.5 E) 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.

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

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24 May 2017, 22:35

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GMATPrepNow 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?

When Ted covers the full distance, Bill has yet to travel for 4 more hours to complete the distance \(\frac{240}{(240 - 4x)} = \frac{(x + 5)}{x}\)
_________________

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?

A) 7.5 B) 10 C) 12 D) 12.5 E) 15

*Kudos for all correct solutions.

Another approach....

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.

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

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23 Oct 2017, 22:22

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This post received KUDOS

GMATPrepNow 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?

A) 7.5 B) 10 C) 12 D) 12.5 E) 15

*Kudos for all correct solutions.

Let Ted's average speed be x miles/hr. Bill's average speed be x-5 miles/hr.

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

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03 Nov 2017, 03:44

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Easier method Bills time be= t and speed=x Ted's time=t-4 and speed=x+5 distance =240 Bill's time(t) = distance/speed=240/x Teds time(t-4)=240/(x+5)

Plugin answer choices. you should start from c or answers which are whole numbers

Let bills speed be =15 we now have Bill(t)=240/15=16 Now Plugin for ted t-4=240/(15+5)=240/20=12 or t=12+4=16. with above approach we can avoid quadratic equation.

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

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04 Nov 2017, 14:19

1

This post received KUDOS

GMATPrepNow 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?

A) 7.5 B) 10 C) 12 D) 12.5 E) 15

*Kudos for all correct solutions.

let r=Bill's average speed Bill: d=rt Ted: d=(r+5)(t-4) combining, rt=(r+5)(t-4)➡ 4r=5t-20 substituting, 4r=5(240/r)-20➡ r^2+5r-300=0 (r+20)(r-15)=0 r=15 mph E