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Bill and Ted each competed in a 240-mile bike race. Bill’s a [#permalink]
06 Jun 2017, 13:00

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Question Stats:

50% (02:11) correct
50% (03:08) wrong based on 8 sessions

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?

Re: Bill and Ted each competed in a 240-mile bike race. Bill’s a [#permalink]
07 Jun 2017, 15:11

Expert's post

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.

Re: Bill and Ted each competed in a 240-mile bike race. Bill’s a [#permalink]
05 Dec 2017, 18:19

Expert's post

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?

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: