Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

74% (02:36) correct 26% (03:23) wrong based on 176 sessions

HideShow timer Statistics

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
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

Show Tags

24 May 2017, 23:35

4

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?

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.

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

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

Show Tags

23 Oct 2017, 23:22

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 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]

Show Tags

03 Nov 2017, 04:44

1

This post received KUDOS

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]

Show Tags

04 Nov 2017, 15:19

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

gmatclubot

Bill and Ted each competed in a 240-mile bike race.
[#permalink]
04 Nov 2017, 15:19